Lecture 8: Quantum Harmonic Oscillator

MIT 8.04 Quantum Physics I, Spring 2013
Instructor: Barton Zwiebach

In this lecture, Prof. Zwiebach covers the quantum mechanics of harmonic oscillators. He begins with qualitative discussion on bound state solutions and then moves on to the quantitative treatment of harmonic oscillators.

License: Creative Commons BY-NC-SA
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[lukelively]

I love this guy. I love when you can tell how much a professor loves a subject.

[CARLOSROMERO-MathFermat]

Solution of the Schrödinger Equation of the Quantum Harmonic Oscillator begins at: 25:30

[drummerboy]

ughhh gosh this is so good. my prof never goes through the mathematical steps like this one does.  this one gives you mathematical insight and reasonable physical arguments.  my prof treats us like we're physicists!

[anugrahmathewprasad]

This is so good.. He explained quantisation so well! Prof. Adams set it up so well in the last lecture and here it just became so clear

[okotray]

I appreciate the online lectures from MIT, especially this professor.

[everlastinGamer]

When the lecture is so good that YouTube viewers clap alongside the live student audience. Awesome, thanks so much.

[chinonsougwumadu]

This is the only professor that makes quantum physics seem like some classical music... sometimes I just watch his lectures lying on my bed.

[robertsalazar]

Hey! I'm retired and watching these lectures for fun! I agree, the instructor's energy should be part of schodingers equation.😁

[Dr.Sortospino]

This professor speak so clear (nevertheless the spanish accent) that you can gain time putting the speed 1.5x :D

[adrianlowenberg]

I am watching this content as a mathematics student, which is interested in physics. I guess this will be the topic of the everywhere announced 8.05, but the quantization follows generally as the Eigenvectors of a Hermitian operator, like E here, are orthogonal to each other, and the Hilbert Space where the Wavefunctions live in is of course separable, so there are only countably many different Eigenvalues, therefore possible energy measurements. This also explains why the Eigenfunctions are a class of orthogonal ploynomials. The physical argument given here is that the Wavefunction must be normalizable, but mathematically this only means that it is in the Hilbert Space, or that it is integrable. What I find most interesting here is the techniques used to gain intuition about the differential equation, and therefore solve it explicitly. I think however that a bigger mathematical background would help many students to know which "rough" solutions are okay and which cannot be. I am very grateful however to see this very different teaching style to the one I am used to for free!

[PrabandhamSriniketan]

Watching this a day before the exam, wish me luck!!!

[kalj]

Very nice and understandable derivation. Thank you!

[DrBouwman]

Wow. Just wow. i wish I could give classes like that

[saskiavanhoutert]

Quantum physics is somehow good explained and interesting by this physician, thanks.

[stefkakannenberg]

Yes. One has to take the solution for the ground state energy level at T=0K from Stochastic Elektrodynamics in order the differential equation to have reasonable solutions. Right. Why not to just calculate with Stochastic Elektrodynamics from the beginning.

[itsanki]

just becuase a polynomial has infinite terms doesnt mean it will blow up at infinity. A simple examle is series expansion of 1/(1+x) for x>=0 has form a0 + a1*x + a2*x^2 + a3*x^3 + but this doesnt blow up at infinity, rather it goes to zero. So it really depends upon the coefficients of the series obtained. We need further analysis to show that the series obtained in this lecture(hermite equation) actually blows up. The result of analysis would be that both of the series grow like e^(y^2) . And the overall solution psi = h*u grows like e^(y^2 / 2 ) . That is non normalisable . So the only way out is that the series terminate.

[flatisland]

36:01 1:05:44 1:13:26 he just swallows it

I like this series! :-)

[flyingbirds]

This video is an excellent video!! I want to thank the lecturer a lot because he made the topic very easy and told in a very beutiful way. Especially the coefficients and exp(u^2) comparison was very very clever and an excellent explanation. Thank MIT ocw very much!!

[indiaview]

After so many approximation finally solution of harmonic oscillator land up on the Harmite Polynomial series...

[sunnypala]

Explained very awesomely helpful.thank you so much