# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

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### Projective representations and cental extensions based on Schottenloher's book

In Schottentloher's book, a theorem is stated: Later on, a remark is made: My confusion comes: Is E always of the form made in the remark, namely are the following to sets equal(up to set theoretic ...
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### Is linear momentum quantized in quantum harmonic oscillator

I'm self-studying QM and have a basic question on quantum harmonic oscillator. The Hamilton is certainly quantized under this model, that is $E_n=(n+1/2)\hbar \omega$, for $n=0,1,2,...$. But is linear ...
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### Experiment design: can one actually measure the speed of non-local light in curved spacetime

The equivalence principle tells us that in some local neighborhood, every free-falling observer in a general relativistic spacetime will measure the speed of light to be $c$; this literally means at a ...
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### Adjoint of the Quantum Momentum Operator

I'm studying quantum mechanics and I have a question about the momentum operator. We have that the momentum operator is given by \begin{equation*} p = -i\hbar\nabla \end{equation*} and so its adjoint ...
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### HaMiDeW coefficients - recursive calculation of the coincidence limits

In his book Aspects of Quantum Field Theory in Curved Spacetime Stephen Fulling calculates the coincidence limit $[a_1]$ and gives an idea of how $[a_n]$ with $2 ≤ n$ can be found recursively. Since ...
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### The spectrum of the Hamiltonian in quantum mechanics

Consider the Hilbert space $\mathscr{H} = L^{2}(\mathbb{R}^{d})$ and a Hamiltonian: $$H = -\frac{\hbar^{2}}{2m}\Delta + V(x)$$ for some potential function $V$. States of well-defined energy $E$ are ...
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### Holley and FKG Lattice Conditions

There's an interesting exercise (page 13, Exercise 11) in Hugo Duminil-Copin's Lectures on the Ising and Potts models on the hypercubic lattice, which states that the following 2 statements are ...
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Consider the bosonic Fock space $F$ and let $a^\dagger$ and $a$ denote the "usual" creation operators. As far as I know, these are defined on the dense domain $\mathcal D(N^{1/2}):=\{ \psi \... • 6,117 2 votes 1 answer 119 views ### Spectrum of$f(T)$, where$T$is a self-adjoint operator Consider on a Hilbert space$\mathcal{H}$a self-adjoint operator$T$with spectrum given by$\sigma(T)=\{\lambda_n\}_{n \in \mathbb{N}} \subseteq \mathbb{R}$(let's suppose for simplicity that the ... • 107 0 votes 1 answer 85 views ### On the domain of$P^2:=-\nabla^2$for the infinite square well A potential of the form $$V(x) = \left\{ \begin{split} 0&\quad \operatorname{in}\ [-a, a] \\ +\infty&\quad \operatorname{elsewhere} \end{split} \qquad a>0, \right.$$ compels us to solve$...
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Consider the bosonic/fermionic Fock space $F^\pm:=\bigoplus\limits_{N=0}^\infty H_N^{\pm}$, where $H^+_N:=\vee^N \mathfrak h$ and $H^-_N:=\wedge^N \mathfrak h$ for some (complex, separable) one-...