The Quantum Harmonic Oscillator Part 1: The Classical Harmonic Oscillator
ฝัง
- เผยแพร่เมื่อ 27 ส.ค. 2024
- For our third quantum problem we will visit harmonic oscillators. In a classical setting, this is like the ball on a spring we examined when learning about Hooke's law in the classical physics series. But this has quantum application as well, in modeling the vibrations of molecules and things of that nature. How do we calculate the energy of such a particle? Let's take a look!
Script by Hèctor Mas
Watch the whole Modern Physics playlist: bit.ly/ProfDave...
Classical Physics Tutorials: bit.ly/ProfDave...
Mathematics Tutorials: bit.ly/ProfDave...
General Chemistry Tutorials: bit.ly/ProfDave...
Organic Chemistry Tutorials: bit.ly/ProfDave...
Biochemistry Tutorials: bit.ly/ProfDave...
Biology Tutorials: bit.ly/ProfDaveBio
EMAIL► ProfessorDaveExplains@gmail.com
PATREON► / professordaveexplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: amzn.to/2HtNpVH
Bookshop: bit.ly/39cKADM
Barnes and Noble: bit.ly/3pUjmrn
Book Depository: bit.ly/3aOVDlT
i know these videos don't get as many views as your debunking videos, but honestly love the purely educational material, and i hope you keep making it.
Sorry for the off topic. Just want to say a big thank you. I am an electronics engineer that hated math with a passion. You explain it step by step and also quickly.
I’m watching this and said to my wife: “isn’t this so fascinating?” And she replied: “oh he lost me at hello” 😂
hhhhhhhhh
😂
Professor Dave Maguire 😂
🤣🤣🤣🤣🤣
My wife too😂
“Oscillation Function, what’s your junction?” Thank you Professor! ^.^
Literally just did this in class, still cool to see it from you though!
Hey professor Dave! Could you please make a serious video on electrodynamics? My mom is having a hard time in her classes. Would be much appreciated
It’s in the works!
Thank you so much!
Welcome to the least toxic part of TH-cam where people are just looking to better there education
I was really waiting for this video...now hope the 2nd part will come soon... thank u so much
Yah it will surely come bro !
Ok this is awesome! Clever derivations and all.
🥉
Our professor is going to explain this law at University tomorrow, so I am Lucky 😏😂
But I am not perfect at English, so I am trying to understand well.😭😂😂
@@user-ly4gy1iz2e Who you mean?
@@user-ly4gy1iz2e his head must've exploded from all of the raw knowledge
Potential vs. Potential Energy question... At 2 minutes you state that F= -dV/dx, shouldn't this be F= -dU/dx (where U is the potential energy)?
Potential would imply either voltage or gravitational potential. The derivative of the former wrt displacement would be the electric field; the latter would be the gravitational field.
So basically, in quantum mechanics, we call the potential energy the potential, so they are the same.
In quantum mechanics, we use a V for potential energy. (Idk why exactly)
Late response, maybe you found the answer already...
hi pr Dave !! your videos are fascinating and helped me a lot. Will you consider making videos on statistical thermodynamics ? This class is incredibly hard and i feel like your vids would clear that up nicely :)
Thank you for this Professor Dave
Great video! But I must point on a tiny error. the second time derivative in Newton's second law is not partial
I love your quantum series
Cool vid! This is useful for my Intro to QM course, perhaps this series will help me better understand the quantum harmonic oscillator solution.
I got thrown off by the solution to SHM equation using solutions to Schrodinger's equation. I think people are much more likely to know the solution to classic SHM than to Schrodinger equation with V=0.
Because it is labelled Part 1, I thought, hey, I'll give it a listen. Let's see how far I get.
Two minutes ... that's better than I thought!
Sir ....big fan of you ❤... From India 🤗
I Hated Differential Equations in collage, Thanks for making the explanation clearer.
Shouldn't Keff be squared???? In your other video (Particle in a Box Pt. I @ 3:37) you multiplied by (-2m/h^2) and subbed k (same eq. in both videos) which had only K^2 x Psi(x)... please help as this seems incongruent. Thank you Professor Dave, love the channel!!!!
You're right. I was looking for someone, who had already recognized this mistake. k²_{eff} = (2mE)/ħ² and this is what needs to stand @7:17 in order to bring the ħ²/(2m) from the left to the right side of the equation (I ignored the "-" here, because because the sign was transferred correctly).
Found another error: @16:21 he said that the total energy of the classical harmonic oscillator depends linearly on the initial velocity of the particle, but it depends quadratically on the initial velocity as is is correctly written in the formula.
This helped me in my physics exam.Thanks alot Prof.Dave!
you're amazing! got learn quantum mechanics for my first exams as a first year chem engineering student XD
Thanks
We need part 2 of the quantum harmonic Oscillator for our Physics Exam this week!!!!!!!! Please!
Hello Professor Dave, have you thought about making a video about light physics (I am not sure what it is called) or like, what Lux, Lumen and Candela are ?
very informative
What happens when the potential is only in the limit 0 to +infinity..but potential become infinity in the negative x axis.
F=-dv/dx meaning??? Can anyone tell me??
"∂" is a "d"?
Kind of but it's for a partial derivative, check my mathematics playlist for review.
@@ProfessorDaveExplains Okay, thanks! I recognized the symbols, though I don't recall ever hearing that symbol called by that name. But it's just been about a decade since I took calc, so I've forgotten quite a bit.
Well ,admit it .Who else replays his INTRO🤣🙋♂️
I always do, it is so catchy :D
I think keff in the equation should be squared at 7:23
Damn right when I needed it !
What if you do that partial derivative with repsect to 't' and there is a 't' in mass that we don't know about? The x(0) stuff kind of looks like the recursive polynomial sequence stuff. It goes in the diagnol matrix, I think. For change of basis. It's kind of a shortcut if you want to multiply A^n.
what is the relationship between planck's constant and the amplitude
thank you
Thanks 🙏
I have a question for when solving for the frequency. Shouldn't the quantity be in the standard units of mass which are in kilograms? It seems like you solved it in grams.
The CGS system is often used in physics. It's a perfectly good system (but the electrical units are weird).
7:31 it should be (k_eff)^2 in the second equation NOT k_eff as it is (coefficient of psi(x))
Also, use K for Kinetic Energy (not T) near the end.
Otherwise, Awesome video.
3rd
The equation should consist of $k_eff^2$ 7:20
thanks
VERY GOOOOD
Why did you only use partial derivatives?
In the general case, the variables depend on time as well as space.
I believe Nikola Tesla was close to inventing a dimensional tuner so to speak. Using 432 hz frequency might have worked. I wonder if he used more than one oscillator directing the vibrations into a single point against each other could've opened a door into another dimension. The guy might had been crazy but he was a genius. It makes me wonder if he used a more powerful source of energy instead of steam. Either way either destroying the world or opening a portal into another dimension would've been worth the risk.
Hello proffesor,can you reply to a bunch of flat earthers that say that the universal gravitation law is wrong
Yeah, drop any object.
@@ProfessorDaveExplains That only works if the gravitational force exceeds the buoyant force.
Yep, which will be true for pretty much any substance except hydrogen or helium.
@@ProfessorDaveExplains Yes, but I wouldn't put it past a flat-Earther to "drop" a helium-filled balloon, and claim that gravity doesn't work.
Teşekkürler
Good
Please in memory of Mrs viced rhino please consider making a charitable donation in her name. Spread the word and thank you 😊
1:23 F equals *minus* k x, not "negative k x". Why have Merkins begun using this terminology? k or x may or may not be negative numbers, or odd or even numbers. Why not say "F equals negative odd k x"? That would be similarly wrong.
Um, no. “Minus” implies an operation. Subtraction. Negative implies a value. If either of the values are negative you can still apply negative to a negative number. It just becomes positive.
please open an Arabic transiation
Can the proffesor explain anything?
@@kirkhamandy I'm a freelance scientist my research luckily involves a small amount of basic maths. I find my work rewarding and purposeful
Lisede bunu öğrenen biz seri üzgün
damn jesus got me A+ on exam amen
60th
👍
570th lol.
First
🥈
cringe
First!
🥇
Setting V=0 is not possible. It describes a particular state of the system where x=0. In short V is not uniformly 0 over the entire domain of displacement.