All Questions

I'm trying to understand how bad things could possibly get without Cauchy completeness as a criterion for Hilbert spaces in quantum mechanics. Obviously, doing calculus on a pre-Hilbert space would be ...

I am having a hard time making sense of the so-called "delta function potential well" in quantum theory. The Hamiltonian operator is defined as (with $\mathscr D_H\subset \mathscr H=L^2(\mathbb R)$) $$...

Let $\mathcal H,\mathcal H'$ be Hilbert spaces (not necessarily separable). A "separable state" is a trace-class operator of the form $\sum_i \rho_i\otimes\rho_i'$ where $\rho_i,\rho_i'$ are positive ...

In a lecture on Quantum mechanics, the professor concluded that if $a$ is a linear operator with $[a, a^\dagger] = 1$, where $a^\dagger$ is the adjoint of $a$ and $[a, a^\dagger] = aa^\dagger - a^\...

I have a problem with understanding how the resolution of the identity of an operator is presented in some literature for physicists. I'm a student of mathematics, and I understand the notion of a ...

I have a simple question I've managed to get myself quite confused about. Given a Hilbert space H, what do we know about the cardinality of (a) the set $P(H)$ of projection operators onto $H$ (...