The time evolution operator in quantum mechanics

📚 In this video we learn about the properties of the time evolution operator in quantum mechanics. This operators provides an alternative but equivalent way to the Schrödinger equation for the study of time evolution of quantum systems.

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Interaction picture: [COMING SOON]

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Director and writer: BM
Producer and designer: MC

[JohnVKaravitis]

Keep 'em coming, and feel free to go both into detail when it comes to typical university material and problems, BUT ALSO please delve into the different intrepretations of QM, and Bell's Inequality. Thank you!

[prikarsartam]

nowadays when I'm having some conceptual trouble I'm coming to your channel. Please keep it this way Sir, you're creating beautiful and precise content here.

Just one slight thing: I think at 14:26, it would've been better to mention that the operator in the exponent gives the corresponding eigenvalues of the summand |u_i> with the power series expansion of the e^{ (-i/hbar)H(t-t') } and the fact that for a hermitian operator (eg. hamiltonian) H^n |u> = E^n |u> when |u> is an eigenstate of the operator.

Thank you by the way!

[stevenschilizzi]

These videos sparkle with clarity, to the point of making often complex topics appear simple. Very energizing! Thank you 🙏!

[miriamstudyaccount]

great video! also love your use of the video description (really helps navigate the videos), and I am actually looking forward to the "Schrödinger vs. Heisenberg picture" video and the "Interaction picture

[rsbenari]

Crystal. Well done, esp the takeaway regarding 'reversing the arrow of time.' Cuts to the quick. Thanks.

[iotaphysics]

awesome explanation...i came here after reading sakurai...and got crystal cleared

[WhiskeyTobin]

Thank you so much for this. I was having trouble understanding some of this from JJ Sakurai and my first semester grad QM class alone. Now we're using time evolution with simple harmonic oscillators in the second semester class and this video is a huge help for me to actually feel like I know what I'm doing (test on Monday!)

The other Professor M professor's videos on simple harmonic oscillators in QM are also a massive help. Thank you to both of you!

[Amandajshack]

REALLY looking forward to that Schrödinger vs. Heisenberg picture video. In fact, I wish it was up now!

[nasirsiddiqui]

wow i wish this existed last year. i was doing a quantum information research project when i was an undergrad and i needed to apply a unitary of the form e^-iHt in discrete time steps to a state vector and had no idea how to. this would have really helped.

[guoxinxin]

So beautiful! Do you guys have plans or have already written a beautiful book like the notes in your video on quantum mechanics? I dream to have such a book. Thanks!

[davidroux]

Your videos are just excellent. Thank you for sharing your hard work.

[DivisionbyZer]

Excellent. Curious if the video with the Dyson expansion has been done yet?

[mehdisi]

Hi and thank you so much for your great videos on quantum mechanics. If possible, please make some videos about qed. Good luck

[paulbk]

Thanks to the team once again for the exceedingly useful and lucid discussion 👍👏👌

[chrisyang]

Hello! If I didn't make a mistake, I believe that for the infinitesimal unitary operator part 11:24, if U(ε) = 1 - iεF, then U†(ε) = 1 + iεF. In that case, U(ε)U†(ε) = 1 + ε^2 F^2, so indeed U(ε)U†(ε) = 1 to first order, in accordance with your video on unitary operators, but I was just wondering if there was not a less approximation-y way to proving that the time-evolution operator is unitary?
In any case, great video!

[WhiskeyTobin]

Any idea when the Schrodinger vs. Heisenberg picture videos are coming? Unfortunately it will probably be too late to be useful for the class I'm taking right now, but so far I'm learning more about QM from these videos than I am from JJ Sakurai. Sometimes it felt like just going through motions until I watched these videos and really started understanding.

[sayanjitb]

Around timestamp 2:27, why did you express |psi(t0)> as a linear combination of two other states (similar for |psi(t)>)? Were those any two arbitrary kets or basis kets?

PS: One request, can you please upload a video on the "Dyson" series!
Thanks

[shrodindsy]

hello thank you for the this great content, can you please elaborate about what you meant when your said the correspondence of the vectors is linear ?

[JohnAlexander-hjnx]

hope You answer me on a video thst was two years ago, when something like an electron or an atom changes their quantum state in a system, the other particles that are connected to them should Also change, , or only changes the one particle that was affected?

[Muhammadusman]

Thank you very much for such a wonderful work