What is Hilbert Space in Mathematics and Quantum Mechanics?

Author: William Gottemoller
Published: Sat 13 Mar 2021
Episode Link: https://podcasters.spotify.com/pod/show/william-gottemoller/episodes/What-is-Hilbert-Space-in-Mathematics-and-Quantum-Mechanics-er1gmm

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