Unitary operators in quantum mechanics

📚 Unitary operators in quantum mechanics are used to describe physical processes such as spatial translations and time evolution. In this video, we discuss the basic properties of unitary operators and how we can transform quantum states and observables under the action of unitary operators.

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Director and writer: BM
Producer and designer: MC

[meatychunkz]

If I found this channel months ago and nor 3 days before my exam, I would be in a much better place! Love the videos and the style, please make more

[assassin_un]

Great video again for explining unitary transformation operators Thank you :)
Keep up on the good work :)

[workerpowernow]

this is great! finally finished the QM postulates play list. Do you have a recommendation for order of playlists to advance through? Thanks

[ericdantona]

Hello, I just found the channel and I'd like to know what is the best order to watch the playlists and videos

[doingrandomshit]

I am so grateful for your videos. It is excruciatingly difficult to find good derivations and explanations of these concepts online without tedious mathematical formulations or the author skipping 5-10 "trivial" steps.

Thank you!

[BruinChang]

Pardon me for so many beginner questions.
Is there any intuition of Exp(operator)? Does Hermitian operator in the Exp(.) has somewhat meaning of a cluster of phase angles? And does infinitesimal unitary operator be treated more as a function than as a matrix? That is, how could I build a matrix (dim > 1) that takes a singe real number as its argument?

[ruben-enjz]

unitary operators are related to symmetries right? could you do a video about symmetries in quantum mechanics please?

[williamberquist]

How were you able to isolate U^dagger |lamda> at 4:58? Is this because |lamda| = 1?

[anubratasaha]

Hi! I see everywhere that the infinitesimal unitary operator U = 1 - i e F. First, why do we choose to have a minus sign and not a plus sign? Is there any physical reason? Like we have a minus in the infinitesimal time-evolution or the space translation operator, why not a plus? Certainly G being anti-hermitian permits both.
Second, when equating U * U \dagger = 1 + e (G + G \dagger) + ..., would we have anything new if we hadn't stopped at e but at e^2?
Thank you!

[hp.basketball]

The mathematical definition is all good. But what does actually mean a unitary operator?

[juancarlosdominguezsolis.]

can i ask what is hopf anomalie in qft?, im looking for hopf alegras and i dont know if this algebras have some relationship with qft., please if you know tell me whats going on. i really love your content.

[DivisionbyZer]

Does the converse hold, ie if an operators eigenvalues are exp(ia) is the operator necessarily unitary?

[simamkhan]

Plz explain coin and shift operators and how they operate on spin up and spin down state

[ashishbhargavkalita]

sir why does the unitary operator change the state

[anoopmis.pandey]

At 05:03 how did you write U dagger as e^{i * phi_lambda}?

[rahulmathew]

Your explanations are really good but you are too fast. Reduce your speed