Hydrogen atom wavefunctions
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- เผยแพร่เมื่อ 13 พ.ค. 2013
- The hydrogen atom wavefunctions are mathematically precise but difficult to visualize. This video presents a few visualizations as produced by commons.wikimedia.org/wiki/Use.... NOTE: there is an error on slide 3. In the normalization constant, the (2/na) term should be raised to the third power. Also, the 3rd edition of Griffiths uses a different normalization convention for the associated Laguerre polynomials than the 2nd edition (used when preparing these lectures). As such, readers of the 3rd edition will want to replace the [(n+l)!]^3 with just (n+l)!.
(This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at th-cam.com/users/playlist?list=...)
As someone who has been trained in mathematics, chemistry, electrical engineering, and quantum mechanics, this is the first time I have seen orbital theory brought together in a consistent way. In particular, the chemistry way of depicting orbitals has always confused me. Your explanation of them as sums of the actual exponentials of the wavefunction is exactly the same relationship as radio waveforms have when represented as complex exponentials at baseband vs. real-valued signals at passband. Bravo.
Yeah that part of adding up the exponentials is taught at our UG level here
Don't about that electrical stuff though
In proper chemistry books, they give you the complex eigenfunctions and then do the derivation to show you how to get real orbitals. A good example is Figgis and Hitchman. I don't really get why he keeps insisting that one is the "physics" orbitals and one is the "chemistry" orbitals. They're the complex orbitals and real linear combinations. We use real orbitals when we're dealing with objects in real space. Don't they still do crystal field theory in solid state physics?
As a 15 year old, I pretty much understand nothing (math/calculus wise) but I'm fascinated anyway. I can't wait to study quantum mechanics. I know it'll be tough, but I feel as though I'll do my hardest to learn this.
When you have gotten to calculus, you can do well at it :P You should also take chemistry, since it uses quantum mechanics. This orbital stuff is shared with chemistry. Calculus 3 and Differential Equations are what you'll need for Schrodinger's equation :P Oh, and don't be afraid of the math. It's not as scary as it seems and you won't be learning it all overnight. You'll be taking multiple semesters before you run into this stuff. So, you'll get through it fine, because you build up to it and get comfortable. (and Modern Physics is hard, but it's not horrible. If you enjoy it, it's not so bad)
Jimmy Amato Thanks for the info, man.
no prob. it's my major in college right now, so just sharing what i've seen. this stuff is the type of stuff you learn in a modern physics class (and can feel scary to anyone). but in college, at this point, you will be surrounded by other people majoring in this and know professors and all of them are willing to talk about it, so... even if u do get confused; you're surrounded by other physicists haha they can help lol
that class is a little above anyone majoring in oragami that is just trying to complete a science credit for general education lol
That passion is fucking gnarly dude best of luck with whatever you choose to study.
As a math / physics guy, part of the reason why I've been learning Quantum is just to understand where the hell all those orbitals we learned in high school chem came from. I finally feel like I get them now - thank you!!
I’m like 3 years out from being able to understand this. There a fragments that I understand and the rest is nonsense. It’s a truly bizarre feeling.
We all are in this together 😪
Best video in a while. I just got done playing video games and was bored, but I loved this video and followed along. The separation of the PDE’s takes me back to a fun time where I was learning math that 95% of the world never sees.
You think 1 in 20 people use PDEs and wave equations?! Have you even been to the DMV?
Bruh im so high
Blazed Physics: Seminar Room 420
Took a Physics 420 class; was not chill, the only thing that smoked was my brain
@@the-fantabulous-g I had a Chem 420 class that was for physical chem. Not fun either
Me too.
@@Justin-ou6gq pchem senior year……?
I don't know why I added this to my watch later, the time taken to understand the things REQUIRED for this is longer than my lifespan.
Not if you cram, and dedicate yourself to learning it. Same with any subject. I always thought science was cool, but there was a disconnect between what I knew, and what I knew that I SHOULD know. So I didn't know much beyond the states of matter, and the basic stages of conducting an experiment, until I dedicated myself, because I wanted to go into the medical field. Now, I understand, and am able to explain things I never knew I would.
Not at all... all he showed were visualizations of s, p and d orbitals.
The math behind them is a bit complex, but that don't matter, the pictures do D:
Haha
LOL No it's not😂😂
I think the most impressive thing about quantum mechanics is that 3 years of university are enough to understand it at a basic level.
I didn't know that about the difference between physicist and chemist depictions of orbitals.
Electron shell calculations for covalent bonds. And probability locality have different uses. Physicist are precision driven. Reality need not apply..Yet.
They read different author..
Thank you. You helped me to understand a little about the wave functions. I am an old chemist.
I am also dyslexic - I mix up right and left, near and far, and up and down. So this is a challenge.
Thank you again for trying to explain a very complex subject.
this video has saved my life in physical chemistry. seriously such a good video thank you !
I like how you made the orbitals look like candy. Good use of color gradients
I'm still 19, still learning differential equations, somehow the video provided me answers explaining these "shapes".
Physicist's explaination had more interesting details. 😉
It's a good improvement for me. Thank you. ❤🎉👌
great video. one mistake is that the radial dependence is actually r^2 times the radial equation( due to the volume integration) which makes the probability 0 to be found at the origin.
That makes a lot more sense
Tony Mayer Yeah that confused me for a while
Yeah bruh... Depiction of Psi diagrams were all good until those statements about "likely/unlikely to be found" came into the talk.
Yeah probability density Max at origin but probability is maximum at far away
Great work, solving Schrodinger into 3-D. Do realize force at 'c' interactions, with photons, electrons in cone duet transmission, cam synchronized positron, neutron, magnetron in the image kinetics, graviton and protons with neutrinos at 'c'.
Thank you for the very comprehensive explanation!
Thank you Sir. I thank you from the bottom of my heart. May God bless you.
this video is somewhat misleading, the wave function he is talking about is the probability density wave function, so this video's wave is finite at r=0. But the probability of finding a particle at r=0 must be 0, or an electron will be captured by the nuclear all the time. | PSI *() PSI ()| r^2 sin (th) was the one she should have drawn.
I doubt you needed to watch this video, but we needed you to watch this video! Thanks for your comment
If it looks like a wave, it is one. The nucleus is the reason for the wave. It doesn't capture the wave, since the outcome is transient in our universe. Also, the electron portal is not described in this presentation. Perhaps, that would be another class. This presentation is great😁.
@@solapowsj25 electron portal ! Sounds interesting ? Would u like to share some (vd/website) to make me understand the gist of that ?
@@solapowsj25 "The nucleus is the reason for the wave"....Did u mean to say that it's quite like the Particle in box problem where the nucleus acts like a high-potential barrier to make the string (the electronic movement) as a wave ,back and forth ?
@@nomadsland7195 I'd give you this concept to grasp. The nucleus has a hammer 🔨 head that smashes into vacuum of graviton, with two up and one down quark of proton. The concentric ripples via neutrons, positrons and finally electron shells burst out through portals to radiate the energy photons at 'c' in free space 🚀. Bohr used the nature of water drops to develop his ideas.
It helps, so I mention.
Thank you so much for making this video!
In the 2nd distribution, would the inner sphere be yellow?
I dare you to take a shot every time he says "equation" or "function".
The Clay Pigeons Don't Stand A Chance .
How did you code this? I need to program a simulation of wave forms. Please share your programming tools used and functions as you have used them.
I looked at the first step and promptly died.
same
There's a 50% chance that u died, but ill measure again!
to break this down extremely simply the Schrodinger equation states this
Total Energy = Kinetic Energy + Potential Energy
Brant, thanks for the upload. DeBroglie waves are said to coincide with the well tempered scale. Was this derived from Schroedinger's equation?
love the visualization!
Fascinating. Is it possible to model an interaction between 2 atoms please ? Thank you 🙏
Is there anyway you can do a diagram for Cromium atom super position. And possibly a Cr2 atom alos?
Euler's equation in 11:35 are with the oposite signs
Amazing. I just might pass this course now.
15:23 was actually really useful to visualize the plots
9:02 nice to meet you fee! i am said!
I dont understand anything, but its cool that you guys do
In the case of (2,1,0) are they 1 pair of concentric spheres, or are they 1 pair of single spheres?
Recommend in understanding physics of Schrodinger in relation to chemical description
Graduate chemistry major here. I got my B.S. in chemistry with a minor in applied mathematics. This stuff is fucking hard lol it’s easy to hear someone else explain it but when you have an Ivy League trained professor teaching you quantum mechanics, it’s fucking insane lol good luck to anyone studying this crap
Dr Branth Carlson.. Thank you very much for your data sharing.. Also I need to understand Hydrogen Bond (Deeply)... If you can help on that subject or not.. Thnks anyway
The cone drawings were good. Sufficiently detailed.
Nice penmanship !
Truely legit question. Are you not talking, in this vid, about Dirac's armonics?
I've read a couple of papers about this Diracs wave functions and what you are showing are those obtained with Diracs equation. Schrodinger arminocs are those like the ones chemists use. While there are ways to obtain Dirac's orbitals with the Schrodinger equation, those are ad hoc corrections.
I really would like to know what you have to say about this. I'm chemist. So really don't know for sure. And those papers were Journal of chemical education (still some of them explained the math behind).
Me, A 14-Year-old student, Who is barely passing physics and hasn't even started trigonometry:
"Hmm yes the Wave Function and a weird fraction"
It has come to my attention that the "weird fraction" is called calculus and I can't wait to fail another part of math.
How many more calculus classes do I have to take before I can barely understand this video?
As far as I remember (from many years ago), energy levels have capacity for 2, 8, 18, 32, 32, 18, 8, 2 electrons. This gives me a max total of 120 electrons. What happens if I want to have more than that? Will level 5 spring up new orbitals and increase its capacity somehow? The obvious reason I'm asking this is for the heavy element synthesis that's going on, and the aims are already at >118 protons.
+Daniel Jesús Valencia Sánchez This is a misunderstanding. For the nth energy level you have 2*n^2 available electron orbitals. They are not filled entirely before starting on new orbitals due to energy. (It's easier to jump to a higher n, rather than to a higher l sometimes.) So yes, the 5th level has more available orbitals (the "g" orbitals). And the 6th level has even more ("g" and "h"). Notwithstanding though, there are predicted issues where the periodic table breaks down anyway due to orbitals filling in the "wrong" order because at these energy levels they're so close together. So chemically these ultra heavy elements will behave differently than their place in the structure of the periodic table predicts. (However, they're so radioactive anyway, that it's a bit of a moot point.)
What is special about the z axis that makes some of the orbitals look different along the z axis than along the other two axes? The spin of the proton or of the electron or something?
great question. The z-axis is entirely arbitrary. We pick it so we can write functions down. But atoms don't care about our choice of coordinates, so how can this be? Someone else can rotate their coordinates and have a z'-axis. Luckily, the spherical harmonics are very special, and if you rotate the coordinate system, they form "irreducible representations" of the rotation group.
That means, your new P orbital becomes a mixture of my unrotated P orbitals. Likewise for the D orbital: Your D'_2,2 is a mix of my D_2,2, D_2,1, D_2,0, D_2,-1, D_2,-2 orbitals. States of different "l" don't mix, just states of same "l" and different "m"....but "m" is the projection of angular momentum on z-axis, so that makes perfect sense.
But can the atom be in these mixed states, I thought it wants to be in an energy eigenstate? Yes it can: all the states of same "l" are degenerate, they have the same energy: the atom does not care how we define the z-axis. Because of that, it won't be in these states by itself, it will be in a mix...
...until be add an interaction. Once we turn on an electric field or a magnetic field, that defines a direction and makes the z-axis meaningful (z is just a conventional choice). The interaction lift the degeneracy and states of different "m" have different energy, and the atom will be in these states, emitting radio photons to transition (at fixed l).
Remember: those wave functions are approximations for a non-interacting, non-relativistic atom. They are stationary: the never change. Once you add interactions, then you use those states as a basis for describing real physics.
Good stuff. What are the chance of that?
So possible wave patterns not connected is where other atoms connect
Open understanding,thanks
amazing video
I seen this in a dream and I couldn't explain it finally someone can show what I see now my question is
It is possible explain the transition to positive to negative whit Vorticial maths?
I liked what you did and I may be a wee bit pedantic to ask to have spins included.
yes, because then it's not Schrödinger's equation anymore. You need to master the Coulomb atom before adding spin and relativity.
@@DrDeuteron its the complex matrix form of the S.w.e. Dirac just factors these 'non swe ' to get the Dirac relativistic electron forms of the S.W.E.
Fractional powers of differential-
integral operators to solve in integral calculus.
@@DrDeuteron thank you for clarifying your concerns.
I was referring to something documented and useful in the hyperfine spectra of electrons using ENDOR.; a patent was written to use the spin and spinor aspects of electrons and holes...
In the quantum computer patent, in 1998 of a condensed matter photonic quantum computer for USAF . A PhD named Hotaling from ny wrote a tech paper on that patent using the ENDOR aspects of microwave and infrared coupled spins do do quantum logics.
By that I mean actual algebras of John von Neumann. They were reduced in this patent to boolean and limited, as such mechanical .
I understand your concerns of getting deep into the weeds of too advanced quantum physics but the resesrches continue from that work on using ENDOR in practical ways using the Dirac properties of matter and magnetics in Soliton physics. Thats what I know. In this time of history quantum gravity in human mind physics such as Penrose
and Hameroff will need the very ideas I spoke of of deeper generalizations of SWE in other operator (del) geometries. Just doing my job.
Can the superposition cause the relation function change?
I'm going to complete it soon
5:48 For the region where R dips below 0, you meant to fill in the part under the threshold but filled in the part above it.
9:54 Isn't the particle only likely to be found at the absolute value of the wavefunction squared like the chemists' representation (and the physicists' representations are about the wavefunction itself, not about where the particle is likely to be found)?
Correct I 100% agree with point 2
We, chemists, are not scared of the imaginary numbers; we use it all the time for FT equations. I think chemists don't find the utility of imaginary numbers in showing the probability distribution of electrons. But I believe we should have been taught to see the orbitals individually in terms of the imaginary parts. The orbital structure makes so much sense. Thank you for explaining that part.
(n,l,m)= (1, 0, 0) is hardly BORING, unless Neil "BOHR"ing! Rather, that ground state BLUE BALL is highly exhilarating in the Context of "The Changeling"! Uhura's "The BALL is BLUEY, Blue "E", Blue e=2,718281828 around its imaginary equator!
Blue and orange are opposite, purple and yellow are opposite just FYI amazingly detailed explanation!
From the future - physics aside, your tablet drawing skills are matched only by professional digital painters.
Nice and interesting video, thank you for posting it!
I am not (yet) a physics student so there are a couple of things I don't get and my teacher hasn't answered me.
For example why are they called the hydrogen atoms orbital representation? Does it matter if the atom is hydrogen or something else? Plus, it's not like you cab excite an electron and knock it to an d orbital state. Or can you?
It's more of "hydrogen-like atom orbitals", meaning only a single electron. Multiple electrons would interact with each other to make the math unsolvably messy (thus they're just approximated), whereas with only one electron everything is "simple" and beautiful :)
But this is just for maths sake. As all orbitals on one shell of a hydrogen atom have same energy there's no use of thinking that the electron is in any one specific of those. If the electron gets excited it just hops to the next shell (ie n increases). The actual orbital become apparent only on multi-electron interactions.
Alia Åsten oh yeah, it makes sense.
Can you use the formulas on the video to make a computer draw them? Maybe it's easier for computers to do the math.
No, the Schrödinger equation's exact solutions from the video don't take those interactions into account. There are other methods to try and calculate the more complex cases as accurate as possible and indeed modern computing power helps tremendously. But they are still using numerical analysis.
Alia Åsten oh gosh it looks Like I still have a lot to learn. It both excites and scares me
I'm no expert either (though I have some background) and I feel the same :). But more of the excitement and I love the fact there's always more to learn.
Thank you.
Wow this is awesome - subscribing.
Brant - Why did you stop after s p d and not describe the shape of f (l=3) orbital ? Too complex visualization, is it ? e.g. Where are the 5f electrons of Uranium atom most/least likely to be found ? esp. within 5s or 7s spherical region ?
How does one distinguish between determing a quantum particle and quantum wave function, AND a mathamatical practice? A Quantum wave function cannot be observed, cannot be independently observed, and the end result is only a vague probability. So what truly exists, an existential view, or an elite view.
Here's a question:
Let's say i have an atom with a 2p1 configuration, if i force this atom in a geommetry that imposes a choice of x-y axes, i would assume the electron would have to be described by a wave function that also reflects the choice of axes, so i'll assume either a px or py orbital is the wave function (let's ignore pz for now, we can force it to higher energies by the correct environment).
What happens if, on top of this, i also add a magnetic field alog z? Surely the electron should have a definite state of ml=+1 (ground state), so the wave function should be donut shaped and "imaginary", but the x-y axes preference is still there.
What will the wave function look like in my scenario?
Or, more generally, when does an electron physically occupy a px/py/pz (real) wave function instead of a p1/p-1/p0 (imaginary) function and what type of wave function describes the electron if absolutely no chemical environment exists and no magnetic field is applied? Since now not even a z axis is imposed, surely there can't be a p0 or pz orbital preference instead of any of the other ones? Would the electron be in a superposition of all 3 possible orbitals? Is it even knowable?
I could hardly understand the full question of yours. But here's what I've made out and I wanna give a talk over it.
1. There shouldn't be any way of choosing the electron to be in a real / imaginary set of orbitals ? In this real world , why would a particle be in a orbital (the nature of whose curve has only been obtained Mathematically on pen and paper) ? Since the superposition doesn't change the energy of those individual orbitals , they always stay in the real sets.
2. Even if no magnetic field is imposed... They'd be in those same px/py/pz orbitals. For 2p1 , it can be in any of them ,because in absence of magnetic field ,they all are equivalent. So why should the electron have to choose ?!
I don't think they'd be in a superposition of all 3 ... It'll stay in one of the p orbitals...The axis is just a letter after all until you give some magnetic field in a certain direction.
(1,1,1), (1,1,0), (1,1,-1) are degenerate. They all have the same energy. They also form an irreducible representation of SO(3), the rotation group (and set of any fixed "l" does).If you rotate the z-axis, they just mix among themselves. For example, if you declare "x" to be your new axis, then:
px = ((1,1,1) + (1,1,-1))/sqrt 2 = (1,1,0)_x and so on.
Once you turn an external field on, the states are no longer degenerate, and if you want to diagonalize your hamiltonian, you pick the z-axis parallel to the field. You don't have to, but diagonal equations are easier. The atom doesn't care what you do, so if you don't, you get the same physics but with messier math.
on m=D , its interesting that Schrodinger's equation can fill the areas , that are visually expressible with points, expressing where the electron could be- or should be , or is not. - or even better where it teleports from a region, to another region. if there is an equation to show us where the electron can be, is their an equation that can show us where it cannot be? m=d looks alot like like a Pulsar , with m= -2, m=2 , m=-1 , m=1 looking like transitional states into the m=d , with m=d being the best candidate for achieving neutral harmonics. ( the same way a Pulsar finds its way into being ) i cant help but wonder if their is further time symmetric math , where their is a parent or static state in time, along with transitional states which m= -2, m=2 , m=-1 , m=1 are showing. what of torsional physics? how does the twisting of space / time effect these visuals ? i cant help but think, that m=d is the actual harmonic, in a balanced state at equilibrium- in other words this is where it actually wants to be. m= -2, m=2 , m=-1 , m=1 , is what we see when its in the process of reaching this equilibrium. self organizing systems are amazing , and i think its important to identify a transitional state, to a parent or static state. like how an electron transitions to higher or lower orbits within an atomic structure. thier must be a parent state, that it finds based on its conditions, as well as transitioning states between those conditions. they are not the same. im just a fellow nerd here trying to understand something way above my pay grade, im not even sure if i can communicate my thoughts properly. forget about m= -2, m=2 , m=-1 , m=1 is what im saying - those are transitioning states. ( important- but where it settles into- is whats most interesting - which is the m=d state ) as far as a visual, just look at a pulsar and compare it visually to m=d , ( since we are on a subject of visualizing ) and tell me what you see. it seems a strange coincidence that they look so similar.
S is spherical. (scalar)
P is dipole shaped. (vector)
D is quadrupole shaped (hence, it looks like a spinning pulsar, which has a quadrupole moment)..or any rank-2 tensor
F is ..octopole?...it's the shape of rank-3 tensors.
....these are the shapes of the irreducible representations of the rotation group with dimensions 1, 3, 5, 7, .... and so on.
They appear EVERYWHERE in physics.
Why Ang instead of radial?
Any diffrential or i integral solution so we found volumetric function of space and time ???😀😃😃👽👽👽😃😃😀😃😃👽👽😃😀
couldn't you put multiple transparent surface within eachother to show where it's stronger within the sphere? this way you get 4 dimensional ish display
What about f orbital?
You're important
Beautyful explain.
The boundaries of the surfaces are typically defined as enclosing 90% of the electron's probable locations.
This is all well and good; however, these equations only apply to position. Since position is dependent upon motion the models are not complete representations of either position or motion.
There is a theorem in quantum mechanics that states that a complete description in any basis is equivalent to a description in another -- in this case, having the wavefunction of the hydrogen orbitals is a complete description and using nothing but these descriptions you could find the momentum, energy, angular momentum, etc. representations. In fact, the energy and angular momentum representations are staring you in the face! (n = energy level, l = angular momentum number).
I was referring the the models themselves - the visualization. A good model describes all values with one complete picture.
@@blangoog I agree. They always say "The D-orbitals are more complicated"...um, no they are not. In the angular momentum basis they are (2,2), (2,1), (2,0), (2,-1), (2,-2).
Is that any more complicated than (1,1), (1,0), (1,-1)????
This is facinating I would love to understand all this cant wait till they make a computer chip for your brain that makes you understand and know everything in the world all at once would be cool I underatand none of this really but i cant stop watching it because its facinating lol wish i would of went to college. For like 20 different things not like i didn't have time iv been out of school for 15 years now and havent done much i could of went to colledge for 6 things by now so for everyone 18 or younger please go to colledge for as much as possible learn like 10 different subjects like math QM space everyrhing that intrests you if you dont you will regret it later in life beleive me there is nothing better than learning i wish i knew everything. I love watching everything about space, planets gases blackholes atoms how everything works and how gases change in a planet as the decay and burn through all there fuel causing them to collapse and create black holes. I also love watching anything on aliens and ancient ailens. Along with genetics DNA all that stuff i woukd love to play around with DNA. And try to cross animals and bring back exstinct animals all that stuff facinates me
You need to plot probability function to see where the particle is most likely to be, which is at bohr radius for 100 and not at origin.
He showed psi(r). What you want it r^2|psi(r)|^2.
Can the equation not be interpreted in Cartesian coordinates?
In working with sphereical shapes cartesian coordinates are horrible to work with
i just have one question: if these shapes represent the space where we can find the electron with a probability of something above zero, then why are the shapes not symmetric in the way that we could tilt them while keeping the core of the atom in the center?
to make it a bit more clear what i mean:
what controles the direction of where the yellow donut(/the plane in which the donut looks like a circle instead of for example two speres) in m=d at 16:11?
i guess no law of nature makes every hydrogen atom be tilted in a specific direction when it comes to their electron-orbitals.
but if there is nothing that makes it impossible for the electron to be in a donut that is tilted a little bit different, then why isn´t that shape actually a hollow sphere instead of a donut?
Hi, I'm a student taking Quantum Physics II and I don't know if what I'll reply is correct so please bear with what I understand for now.
Keeping in mind that these can be called "probability clouds", we can't just simply tilt the shapes since they are structured to be dependent on r, \theta, and \phi coordinates. If it doesn't bug you enough, try to work the final form of the Spherical Harmonics. It was shown that it was too messy, and tilting these shapes mean that we should change the wavefunction a bit, say an extra angle \alpha to be added to the \theta component.
thanks for your answer.
still:
but there has to be some thing outside the atom responsible for why the donut has a whole to look through it from up and down instead of left and right for example. what is that thing?
whose coordinates are the ones you talk about?
if nothing controles the direction, then isn´t the direction of the donut also just dependant on randomness? which again: would mean that the real probability of an electron being in a place where the donut would be if it was tilted was above zero, therefore the donut should actually be a hollow sphere.
I am not sure, if I understand you correctly
There is no such coordinate system in nature. So if you have 2 hydrogen atoms side by side, then the donut of one of them could be rotated with respect to the other one.
It is just, that we do not take some orientation into account when doing the math, because
a) it makes no difference. The donut is still a donut, but rotated in space
b) the math would get tremendously complicated when you want to deal with arbitrary orientations in space
Thus we just say: hey lets assume a fixed coordinate shape, do the math there and agree, that we can rotate and reposition this result into any orientation or point in space without changing the result. You can do this in the same way as you can rotate your laptop infront of you, this does not change the video you are watching.
Or maybe a somewhat better analogy would be:
imagein a shoebox. looking at the inside you notice that at one corner 3 edges meet. You may want to label them: x , y , z
Now you have a coordinate system, which allows you to mark points inside the shoebox WITH respect to the coordinate system you have attached to the show box. You might eg want to put some object into the box and remember the coordinates of the object WITH respect to the showbox coordinate system.
But of course you can put this shoebox in any way you like onto your table. You might want to rotate it, maybe upside down, move it front back left right. Any orientation or position is possible.
Now: if you look at the object, it has some weird rotation or position when looking from your point of view. But from the point of view of the showbox coordinate system, nothing has changed. The noted object coordinates with respect to the showbox are still the same - with respect to the show box.
SO if you have eg. 2 marbles inside the show box and you measure the distance between them you might say: with respect to the shoe box coordinate system (I have intruduced arbitrarily) the distance between them is: on the x axis 2 inches, on the y axis 1 inch, on the z axis 0 inch. Repositioning the showbox does not change that. They always will have that differences in the coordinate system of the show box, no matter how the box is rotated on the table.
So: coordinate systems are not something absolute. There is no such thing as a universal coordinate x,y,z coordinate system in nature.
kallewirsch2263 you did not understand my problem:
again:
if NO REAL THING dictates in what direction the donut is tilted, then the ACTUAL LIKELYHOOD of an electron being in a place outside the donut but inside anywhere where the donut would be if it was tilted is as big as within the donut.
so the real probability cloud is NOT a donut.
if i am not mistaken somehow, which i probably am since noone else sees that problem, but then i do not see WHAT my misunderstanding is.
@@davejacob5208 Dave Jacob Dave Jacob you make sense. I hope that this isn't just some bupkish answer. My understanding, and theory of an answer for you is definitely not mathematical really. More speculation from my point limited knowledge.
(P.s for the donut, if you change it's rotation (via the z-axis) you change it's state, the torus(donut) can rotate along the x/y axis only in this position)
What influences an electron here however? Likely photons, and because of schrödinger, our observation. Photons are fast (constant speed), and almost always interacting with atomic particles hitting them and bouncing off. (Try comphrending how many atomic particles a photon interacts with before it gets to your photorecptors) An electron is constantly getting bombarded with photons but omnidirectionnel (because light isn't monodirectional), changing it's orientation, and probably position in this probability cloud. It wouldn't be until we observe the electron from a single photon (which would require an observer to immediately observe the electron after the photon interacted) (which would be pointless btw unless we could see 4d and observe the entire particle instantly) that we could determine it's position.
(Not sure if needed btw, but the atom is at the center of donut)
So px and py is not as same as pz?
So is all the stuff they teach in chemistry about the periodic table involving orbitals, electron shells, etc. just a rough approximation based on what hydrogen can do (i.e. ignoring the effects of extra electrons)? Or is there enough mathematical basis to justify saying these shells exist in these specific shapes in, say, an iodine atom?
Yes there is enough of a quantum mechanical basis on why for higher elements the same structure can be found. Electron-electron effects are essential to chemistry, so we do not ignore the effects of extra electrons.
Which course
Yes
Why tf am I watching this whole thing, I'm a bio major who barely passed calc 2.
Cyanopteryx I relate too much lol
I understand this and haven't done calc2 even :^L.
Your comment is litarly the universe echoing my inner thoughts as I gave up on the math and started scrolling down the comments lol
I know the feeling, « blue wings ».
I'm just a lowly Biochemist ;w; The only thing I know about are orbitals, and that was back in Ochem 2
I was so close to understanding all of this, but I don't know calculus or any of these variables except i and pi... I guess I have plenty of time to learn before collage anyways so it doesn't totally matter.
Zach Ward um, if you don't at least know calculus, yet you were close to "understanding," then you must not have been paying attention...
Marcus Laurel I mean close in a more relative way, like if I knew calculus I think I would have gotten it, but in a more general sense, it made sense to me.
@@Morgan-bo1mr they problem with that is whether it makes sense or not, the math, if done correctly, will always tell you whether you are actually right or wrong. Intuition gets you very little in nature.
Hydrogen NLM looks very different from Care NLM.
"LIFE SAVORS A PART OF LINING! LIFE SAVERS!": That was the TV Commercial in 1972-73! If the Life Savers candy roll still is being manufactured as a mouth melting candy, the multi-colored LIFE SAVER of the full color spectrum ought to be manufactured as the Rigibev of the unified but unmixed multi-flavors LIFE SAVORS Candy (Roll) in honor of the "m=2; m=-2 of the hydrogen atom wavefunctions!
Rigibev?? Red indigo green indigo blue ...eggplant... violet?
Did you think ROYGBIV was just a noise? 😂
why there are different normalized constants....
why we use only spherical co ordinates nd y not Cartesian
you reduce the number of co-ordinate to express
We use spherical coordinates because the potential depends only on r, which allows us to separate off an angular part that contains no dependence on the dynamics at all. Thus we 'concentrate' our view of the dynamics into the radial equation. The angular part, leading to the spherical harmonics Y_l^m(theta,phi), does not depend on V at all, and is much more general than the hydrogen atom context. It expresses the mathematics of how objects rotate in three dimensions.
This is an example of a quite general approach in physics to exploit symmetries of a physical situation. There are wonderful mathematical tools (group theory) to get the mathematical form of physical entities in the presence of more complicated symmetries. Great stuff. Leads to the mathematical structure of the Standard Model of elementary particles, and much more.
The potential depends on r, not Cartesian coordinates
.... but of course you could express everything in Cartesian coordinates also, if you want to.
In this case: good luck with the math!
Cool. Now do it for uranium.
Great 😁.
I find it quite annoying that the "virtual" pen is oriented as if you were left-handed. All the time I keep thinking that there's something wrong.
pitthepig, put your viewing device in front of a mirror, and look at its reflection. Voilà, problem solved. Of course, all letters will be reversed as well, but hey, you can’t have it all. ;-)
14:06 - Is that what atoms look like?
Do helium
So chemists lied to me. Noice.
They simplified it so you could use it, you're welcome.
8:35 that made me rolling!!!
honestly don't know if it's good or bad that there weren't any f-orbitals
there are f orbitals. 7 of them.
I’m a “creative,” and have always struggled with math and science all throughout life. So can someone please translate what he is saying in laymen’s please.
Me every 12 seconds while watching this:
what?
pretty pictures
Hariyana utensils show that same structure and ultimately it going to become Shivalinga of indian temple
This is really easy stuff too lmao were just looking at a hydrogen atom...not collider physics and quantum fluctuations
hydegeren miuplates time no matter 1+1- it has no standard
No matter how much you know about this.....YOU WILL NEVER BE ABLE TO MAKE IT USEFUL. #SMARTMONKEYS
@@DrDeuteron No, I'm not kidding.