What is a Hilbert Space? | Quantum Mechanics
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- čas přidán 31. 05. 2024
- An informal, non-rigorous, but (hopefully) intuitive look at what a Hilbert space is. Essentially, it is a complete, normed, inner product space, as opposed to a Banach space, which is a complete, normed, linear (vector) space. What does all this mean? Watch the video to find out!
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References and Resources
Video series on topology and manifolds by XylyXylyX
• What is a Manifold?
A Brief Introduction to Hilbert Space and Quantum Logic
www.whitman.edu/Documents/Aca...
Hilbert Space and Quantum Mechanics
quantum.phys.cmu.edu/QCQI/qit...
Lebesgue Measure and L2 Space
www.math.uchicago.edu/~may/VIG...
Metric and Normed Spaces
www.math.ucdavis.edu/~hunter/...
A Brief Guide to Metrics, Norms, and Inner Products
people.math.gatech.edu/~heil/b... - Věda a technologie
I'm an aspiring Mathematician and I totally love your video.
It would have been good if you would have uploaded this video with higher resolution. If possible, please do it.
As a lay mathematician… ur piece was pitch perfect. Many thx
Great explanation
Great video!
Super helpful video! I'm about to start a class in quantum computing which is a little above my pay grade, and needed a little refresher on Hilbert spaces for it. This did the trick!
Awesome. Good luck in your class!
To make the idea of nearness (neighborhoods) in the topological space more clear, we can loosely define them as follows:
P is an element of X (P ∈ X), S is a subset of X (S ⊆ X), and P is an element of S (P ∈ S)
If Q is an element of S (Q ∈ S) then Q is in the neighborhood of P
And if U = S∪R then U is also a neighborhood of P
Also, the inner product space must satisfy the parallelogram law: en.wikipedia.org/wiki/Parallelogram_law
||x+y||^2 + ||x-y||^2 ≥ 2*||x||^2 + 2*||y||^2
wow, amazingly explained.
Thank you, I'm glad you found this video useful.
BENAKH!
Amazing, it’s same in Klingon!
Great to see the bigger mathematical picture, but I miss the bigger physical picture: why QM? + why QM isn't sufficient?
Pronunciation of the name 'Banach': upload.wikimedia.org/wikipedia/commons/a/a6/Pl-Stefan_Banach.ogg
The "b-nak" space kinda hurt my feelings. It's banach, ba is of normal length and you say the a and the nach is ch not k and the second a is pronounced quickly. So basically banach with emphasis on the first a
Just realised i was one of 11 comments, so i have to add that speaking german fluently banach pronounced bnak kinda hurts my feeling, but the video in itself is very good. If i'm critiquing the pronounciation and nothing else, it might even be a compliment. Thank you for the video