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What is Hilbert Space in Mathematics and Quantum Mechanics?
Manage episode 288628597 series 2902423
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In this episode, we will be covering Hilbert Space and its importance in quantum mechanics. Please cut me some slack because this topic combines abstract algebra with advanced calculus, both of which I do not know. The history of Hilbert Space and the application of it into quantum mechanics should be simple, but its application and derivation surrounding mathematics will likely stump me; I know the English language, but not integrals and multivariable vector calculus. But anyways, let’s explore the foundation of something I do not understand and the foundation of quantum mechanics, Hilbert space.
References:
Hilbert Space - Quantiki
https://www.quantiki.org/wiki/hilbert-spaces
Hilbert Space - Wikipedia
https://en.wikipedia.org/wiki/Hilbert_space
Vector Calculus - Wikipedia
https://en.wikipedia.org/wiki/Vector_calculus
Euclidean Space - Britannica
https://www.britannica.com/science/Euclidean-space
Vector Calculus
http://hyperphysics.phy-astr.gsu.edu/hbase/vecal.html
Quick Hilbert Space Video - Physics World
https://www.youtube.com/watch?v=zASzj4DkZXY
Hilbert Space - Britannica
https://www.britannica.com/science/Hilbert-space
Functional Analysis - Britannica
https://www.britannica.com/science/functional-analysis-mathematics
Vector Fields - Wikipedia
https://en.wikipedia.org/wiki/Vector_field
Probability Density Function - Wikipedia
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