Learn the Basics of Hilbert Spaces and Their Relatives: Definitions
Feb 16, 2018 · Hilbert spaces are at first real or complex vector spaces, or are Hilbert spaces. So all the theorems and definitions of linear algebra apply to the finite-dimensional ones and many to the …
What Distinguishes Hilbert Spaces from Euclidean Spaces?
Oct 23, 2013 · The discussion clarifies the distinctions between Hilbert spaces and Euclidean spaces, emphasizing that while Euclidean space is a finite-dimensional Hilbert space, not all Hilbert spaces …
The 7 Basic Rules of Quantum Mechanics - Physics Forums
May 11, 2019 · The following formulation in terms of 7 basic rules of quantum mechanics was agreed upon among the science advisors of Physics Forums.
The Difference Between Euclidean and Riemannian Spaces
Dec 26, 2013 · Riemannian manifolds can possess various positive definite metrics, and not all Riemannian manifolds qualify as Hilbert spaces. The conversation highlights the importance of …
The History and Importance of the Riemann Hypothesis
May 21, 2022 · David Hilbert and Pólya György had already noticed that the Riemann hypothesis would follow if the zeros were eigenvalues of an operator where is a Hermitian (i.e. self-adjoint) operator, …
Superdeterminism and the Mermin Device - Physics Forums
Mar 20, 2022 · Explanation of statistical independence and superdeterminism using the Mermin device. Superdeterminism simply means the particles must have known at the outset of their trip whether to …
Difference between configuration space and phase space
Sep 4, 2018 · The discussion clarifies the distinction between configuration space and phase space in the context of Lagrangian and Hamiltonian mechanics. Configuration space utilizes generalized …
Refractive index(n(ω)) calculation: Kramers-Kronig relations
Feb 19, 2011 · The discussion focuses on calculating the refractive index using Kramers-Kronig (KK) relations from experimental spectral data. Users express challenges in implementing this calculation, …
Derivation of the Einstein-Hilbert Action Abstract Most people justify the form of the E-H action by saying that it is the simplest scalar possible. But simplicity, one can argue, is a somewhat subjective and ill …
2 Hilbert-Schmidt Operators Definition 2.1 A bounded linear operator K : H1 → H2 is a Hilbert-Schmidt operator if for an orthonormal basis {eα} of H1 the sum P ||Keα||2 is finite.