Coherent state wave function || Concepts

📝 Problems+solutions:

📚 Coherent states of the quantum harmonic oscillator are those states that most closely resemble the classical oscillator. In this video we explore this from the perspective of the wave function of coherent states. We find that it has a Gaussian shape, which is consistent with the fact that coherent states are minimum uncertainty states. We also explore the time evolution of the coherent state wave function, revealing the back-and-forth motion that we traditionally associated with harmonic oscillators.

0:00 Intro
4:16 Coherent state wave function
8:06 Minimum uncertainty state
9:40 Displacement operator
11:02 Time evolution
14:31 Wrap-up

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⏭️ WHAT NEXT?

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Director and writer: BM
Producer and designer: MC

[WilliamDye-willdye]

The animation at the end really helped me.

[asdfmy]

Amazing video, I hope your channel gets the recognition it deserves guys <3

[meetghelani]

such a concise and understandable series on coherent states, thanks a lot!

[DavidRoux-uvbl]

What an absolutely brilliant lecture. The animation is priceless. Thank you so much for all your hard work.

[erikdiaz-bautista]

Excellent work!! Nice videos!! 👏 It would be nice to show how a coherent state looks like in phase space. 🙂

I hope these videos motivate students to learn more about the quantum world, specifically about coherente states because they are useful in quantum optics, for instance.

I work in problems related to the coherent state formalismo in quantum mechanics and it's very nice to find videos that explain it in a simple way.

Regards! 👋

[liulinxiycss]

working on my research project on modeling of qubit dynamics, your lectures on these concepts definitely aid in my understanding! Thanks!

[xinyanxiang]

Very elegant！ I check both math and concept videos. I enjoyed them!!

[soheilcyrus]

hello from university of Tehran, I am a student of Quantum optics and I should admit that I wouldn't understand my courses well without your videos. I appreciate it so much.

[朝鲜高官]

Spend the whole afternoon watching all the videos in coherent quantum states. These videos help me a lot, thanks!
By the way, do you have any pdf files which contain the notes appeared in videos? I think that it will be easy for people to consult when forgetting.👀
Thank you!

[paulbk]

Highly enriching and engaging and learning experience

[monissiddiqui]

Thank you so much for this series! I was just working on an optional problem set on coherent states but there were no lecture materials or textbook readings on the topic ( and no solutions to the optional problems either =/ ). These videos saved the day 😃

[zainkarriem]

These videos are amazing and I found them particularly helpful for learning quantum optics. Thanks so much for making them. Coherent states are theoretically interesting, but do you have a good example of where a coherent state is experimentally created and observed in a physical system? Thanks again!

[danielegiunchi]

can you do also for squeezed states wavefunctions? Both for vacuum state and for displaced squeezed states

[mohammadg.merdan]

Excellent video, It is amazing. Please, could you tell me, how do you display text and equations in hand writing mode?

[FlintPet]

isnt there a sqrt(n) and sqrt(n+1) missing in the beginnign?

[entertainingasap]

it really helps a lot, thanks for wonderful video. Also can you share us code that you have written to draw animation on mathematica

[-ds]

In last animation what would be happened if displacement operator is act on ground state Gaussion wave function

[sreerampg]

Nice! I came here to get a physical intuition about coherent states. So coherent states move like their classical counterpart, with the center of the Gaussian at the expectation value of the position operator. Let's say, if I can look at both the classical and quantum oscillators simultaneously, then the center of the coherent state Gaussian and the classical particle will fall on top of each other as they move?

[bahram]

hi im sound engineer i have question about quantum
how i can quantize the air molecule around my speaker