From the TISE in 3d to spherical harmonics
ฝัง
- เผยแพร่เมื่อ 13 พ.ค. 2013
- Separation of variables applied to the time independent Schrodinger equation gives an angular equation with spherical harmonic solutions. (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=...)
I started today with a quantum intro course starting here. I got freaked out by this griffiths chapter. Some friend of mine recommended this to me but you solved essentially most questions that I had and in hindsight you made me understand previous parts better.
Thanks man, it's very clear. Even clearer than griffiths himself and he is very clear
m and l are actually the quantum numbers where m is the magnetic quantum number giving the number of degenerate orbitals and l is the azimuthal quantum number giving which subshell were talking about (s, p, d or f)
These videos are really Legendre-ary! Thank you for sharing these videos.
😭🤣
38:25 an easier to read depiction of spherical harmonics can be obtained by using saturation instead of value of light for the magnitude of the functions. So, the highest magnitudes would be represented as fully saturated colours, and low magnitudes would appear as mostly white (instead of black). I devised such a scheme, around 23 years ago, in order to represent said harmonics upon a sphere.
thank you for saving my semister 😍
Thanks! You might have just saved my quantum mechanics course with this video!
And what have you done with it?
That was excellent! Well done! Such a beautiful concept in my opinion!
question: at 15:03 after you have divided out (- hbar squared RY over 2 m r squared) shouldn't r squared be canceled out? should you not have (1/R)dr(r^2dR) ? thanks!
Yup
@@navneetmishra3208 yes. No r squared. Teacher forget r squared. I forgive you.
I have been having trouble grasping the concept of spherical harmonics for days!!! My textbook didn't help in clarifying the mathematical details, as it mainly focused on the physical and experimental implications of mathematically predicted 'orbital configurations' (which were derived via spherical harmonics). This video helped clarify a lot of the mathematical components, which I was too lazy to research myself. THANKYOU FOR YOUR INSIGHTS!!
Thank you for these lectures, these make so much more sense!!
Mistake at 14:17
the r^2 term should have cancelled out
nevertheless this video kicked ass
King Crocoduck perhaps you can do a video giving a foul mouth explanation of the rigid rotator as you did with the harmonic oscillator :)
@@MisterTutor2010 4 years ago you were triggered.
@@matthewlemke5310 What are you talking about? That video was hilarious.
@@matthewlemke53109 years ago lol
How are you guys holding up?
Thanks for such an amazing lecture..!!
Amazing, just check the comments for certain errors or keep the Griffiths book next to you to verify. Thank you for the video
thanks for this video,you are a legend
Answers to your questions either in your video description or as a comment is the only thing these videos are missing to really check our understanding.
Thank you so much for everything though. You've done more than enough and it's greatly appreciated.
Attempted Answers:
Find P(1,1) (cos(theta)) = sin(theta)
P(7) = 0 at 7 different points
P(4,7) = 0 at 3 different points - This one is pretty much a guess, not sure how to compute.
m = -3 then l = 3, only allowed value
Awesome 😎
I think if M=-3, L can be greater than 3.
I didn't quite get the reasoning of spherical coordinates not being independent of each other which causes the laplacian to be complicated. It was that vector r changes if you change phi for example. But r is just the distance right not the vector?
14:17 that term should be 1/R, not 1/Rr^2. The r's from the Y/r^2 and -h^2/2mr^2 cancel each other. Still, a great video.
wow, only thing sad here is that ive only dicoverered this channel now. thanks for the vid, you explain great
09:00 Are you sure about that? If the X part is a constant, then they Y+Z part is equal to the same constant with a negative sign. But X and Y can still change in various ways, just independent of x, right?
What do you mean? The 2nd derivative of X multiplied by the inverse of X, is only equal to the negative of the sum of the 2nd derivatives of Y and Z respectively, each multiplied by their respective inverses, when the potential energy equals the energy eigenvalue.
Awesome lecture 👍
Great explanation 10/10
thank you
In 36:10 . Just out of curiosity, how do you get the normalisation factor from evaluating the double-integral underneath???
It's the same as the normalisation integral for more familiar Cartesian coordinates, except we are now in spherical polar coordinates, so dxdydz -> r^2sin(theta)d(theta)d(phi)d(r). I think you can just grind through this by plugging in (Y*Y) . This may be done in more detail in Griffiths Intro or try googling Jain QM pdf and it's done in there.
Wow, this really helps~~ thanks!! :))
Thanks 💜
why isn't at 22:30 the phi function an arbitrary sum of opposite exponentials as opposed to just one exponential
nonetheless m ends up a whole number
I think you meant r^2*sin(theta)*dr*d(theta)*d(phi)
at the 38 minute mark (approximately)
By the way, thank you for the amazing videos. You're great!
Oh my god I love you so much
Is there somewhere I can find the solutions to the check your understanding questions at the end? I've done these on all the vids but haven't been able to check them
superb
THANK YOU SO SO MUCH
37:58 isn't it r^2*dr*sin([T])d[T]*d[F]?
+inperatieloos I think d(Omega)=Sin(T)d(T)d(Phi) so here he integrated over omega, not considering radial part
Wait why do they have to be constant?
+fcmilsweeper9
Without context, I think in the case you think about both describe the energy of the same system.
one thing I didn't understand
what are "pheeta" and "phi" here
Solutions of the wavefunction in spherical polar coordinates split into the dependence on pheeeta and phii.
Edit: you can also solve for the r dependence but is less important in angular momentum which is... well, angular.
22:18 how
Why spherical coordinates?
Orbitals can be described in terms of spherical coordinates.
Why do you describe your room with Cartesian coordinates? Because it is rectangular.
Why do we describe the "room" of an electron with spherical coordinate? Because it is spherical (most of the time), they think.
29:11
0
Plot out cos(x) for 0 cos(pi)=-1.
Thank you
why cant weee just stick to cartesian.... jk spherical reveals nice intrinsic proterties of QM
28:31, fractional derivatives exist so idk about that.
If m is not an integer the phi dependence of the wave function won't be single valued and our boundary condition which is Φ(0)=Φ(2π) won't be satisfied.
Also fractional derivatives are extremely advanced stuff. This is an *introduction* to quantum mechanics which is for undergraduates.
I've found this article, I hope it answers your question :
en.m.wikipedia.org/wiki/Fractional_Schr%C3%B6dinger_equation
Although I haven't understood a single word😂😂
My brain hurts
Bruh the way you write partials is wildly distracting.