Coherent states in quantum mechanics

📝 Problems+solutions:

📚 The coherent states of the quantum harmonic oscillator are defined as the eigenstates of the lowering operator. This seemingly simple definition leads to a plethora of properties that make coherent all-important. For example, they are the states that most closely resemble the motion of a classical harmonic oscillator, and in this context they are called quasi-classical states. As another example, they play a key role in the study of quantum optics. In this video, we define coherent states and investigate some of their most basic properties.

0:00 Intro
2:41 Definition of coherent states
4:16 Coherent states in the energy basis
12:04 Time evolution of coherent states
16:19 The raising operator has no eigenstates
21:04 Wrap-up

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⏭️ WHAT NEXT?

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Director and writer: BM
Producer and designer: MC

[A.p.p.y]

These 22 mins my prof 3 hours lecture on coherent states :)

[sandippaul]

This is literally one of the most beautiful videos on youtube. Another one was "But what is Fourier Transform?"
Really really can't thank you enough for this Bbbrilliant and lucid explanation.🙏🙏🙏🙏🙏

[mariak]

I think there’s a minor mistake at 4:40, doesn’t the the scalar product for the coefficient c_n need to be the other way around? c_n = <n|a> ?

[volkerjung]

can't stop binge watching these videos. I'm so grateful that you guys spend so much effort in making these videos. Thank you!

[A.J]

I am taking a quantum optics course with Prof. Immanuel Bloch at the Max Planck Institute of Quantum Optics, and your videos are life saving. Thanks a lot.

[andrewdirr]

As a university student in physics, I would like to say thank you very, very much for taking the time to make this video (and the others on your channel). I wish I had discovered your channel sooner; it is wonderful. The clarity in your lectures is the kind of clarity that I hope for my own lectures to one day have.

As a student of multiple disciplines, my experience has been that physics professors can have a harder time clearly communicating. The field seems to attract more introverted types and the language in which it is "spoken" (mathematics) can, at times, require such a high degree of complexity and abstraction that it naturally becomes more difficult to verbally communicate. That is an unfortunate confluence of factors, because it is precisely the abstractness and complexity of physics that demands of its communicators that they be especially well-versed in written and spoken word, in structuring information, knowing audiences and tailoring material to them. You do a wonderful job with all of that. A true enrichment to the field. So, again: thank you very, very much.

[YossiSirote]

Great video. One technical error at 4:33 c_n(a)=<n|a> not <a|n>, which is the conjugate.

[noelmanuel]

Excellent explanation..gave a better intuition abt coherent states ..thank you ma'am ❤🔥🔥🔥🔥

[satadrudas]

This channel is just amazing. You guys explain these topics really well.

[suraj.k.gaikwad]

Please do videos on Concepts of Statistical Mechanics as well as Classical Mechanics. Your video clear the important concepts in Physics. Thank You so much.

[asmaa.ali]

Great! keep going on!
at 21:00 the raising operator has not coherent sates as eign states because the reason you said earlier due to the form of the coherent state with sum goes to infinity but NOT because of being not hermitian .Thank you so much

[felipechoy]

I'm in love with your Channel! It is helping me too in my last year as an undergrad physics student.

[paulbk]

One of the most beautifully presented lectures on coherent States of QHO....a great learning experience

[lixianghe-tfro]

Is there an error at 4:46 ? |α>=Σ|n><n|α> so C(α) may equal to <n|α> rather than <α|n>?

[sumaiyaseif]

What I have been looking for, thank you

[qbtc]

This video is so clear and at the level of a junior/senior college QM class. Well done!

[manujsharma]

Thank you for such a wonderful explanation

[mtripledot]

Absolutely brilliant! This will helpe a ton with my undergrad project!

[vicerto]

Thanks a lot!! Hope you guys make more videos on QM topics, i love step by step explanations like these! Greetings from Chile

[MrOvipare]

This litterally cannot be any clearer than this. Thanks for explaining how the coherent state is an eigenstate of the annihilation operator.
It also contextualized how the number states are in the energy basis, which is made up of number states that are the eigenstate of the number operator.
Would it be right to think, with quantum wave-particle duality in mind, that the energy basis is the basis of "counting" in the particle-like sense and that coherent states are in a basis of "propagation" and wave-like behaviour? They describe the same "object" which is a quantum field, but in different perspectives/bias.