From memories of a quantum mechanics class and Wikipedia: In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundament …

Find a (presumably, generalized hypergeometric-based function $f(n,a,k)$), yielding for $n=1, a=\frac{1}{2}$,the rational function (ratio of fifth-degree polynomials) \begin{equati …

I have a Hilbert space of quantum density matrices written in the Glauber-Sudarshan P representation - ie. we have coherent states $|\alpha \rangle$ and we write density matrices a …

Let $(M,\omega)$ be a compact symplectic manifold and $(L,\nabla)$ a prequantum line bundle. There are two schemes to quantize this data: Choose a polarization $P$ of $M$ and de …

My undergraduate advisor said something very interesting to me the other day; it was something like "not knowing quantum mechanics is like never having heard a symphony." I've bee …

There is a well-known theorem, firstly obtained by Denes Petz, in quantum information theory, which is described as follows: $\mathbf{Theorem.}$ Let $\rho$ and $\sigma$ be two sta …

I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta …

I need to read this article "On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups" au …

From the mathematical point of view, where is the idea of the incompatibility between functional analysis, at the basis of quantum mechanics, and differential geometry, at the basi …

I'm currently working through Dirac's book The Principles of Quantum Mechanics. In it, he describes the nature of superpositions and at one point states: "... if the ket vector c …

Is there anyone who studied on the book "Solvable Models In Quantum Mechanics" by Albeverio? I don't succed in understanding the proof of page 116 about the eigenvalues of the Hami …

I am trying to find proofs of the stability of an atom, says, for simplicity, the hydrogen atom. There are positive answers and negative answers in various atom models. The naive …

There has been already several questions asking for an introduction to quantum mechanics for a mathematician, but this ons is slightly different, and more restrictive. I know (some …

I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows …

The free resolvent in $\mathbb{R}^3$ has this rapresentation: $$(R_0(z)f)(x)=\int_{\mathbb{R}^3}\frac{e^{i\sqrt{z}|x-y|}}{4\pi|x-y|}f(y)dy$$ with $\Im\sqrt{z}>0$. So its integral k …