# Tagged Questions

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### graded generalization of the Moyal–Weyl product

Has anyone written about the graded generalization of the Moyal–Weyl product/star product, that is, where the original algebra is already graded? Is it just a matter of signs?
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### Some explanation about Dynin's formalism

I have seen this claim on the Wikipedia page for the Yang-Mills Millenium problem by Alexander Dynin. He is a mathematician working at the Department of Mathematics of Ohio State University and so, I ...
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### Mathematical equivalent to ladder operators?

A powerful method in theoretical physics are ladder operators. They are used in QM to solve problems like the harmonic oscillator and the hydrogen atom. The idea is to solve with their help the ...
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### Integrals of two Bessel functions of the first kind and a modified bessel function of the second kind

I'm searching for a suitable (hopefully simple enough) solution to the following form of integral: $$\int_0^\infty \mathrm{d}x~x^n J_\nu(a x) J_\nu(b x) K_\mu(c x)$$ Where $n$, $\nu$, and $\mu$ are ...
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### Lie group about the quantum harmonic oscillator [closed]

We konw that in quantum harmonic oscillator $H=a^\dagger a$, $a^\dagger$, $a$, $1$ will span a Lie algebra, where $a, a^\dagger$ is annihilation and creation operator, $H$ is the Hamiltonian operator. ...
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### A “coarse” version of position operator and its properties

I am wondering if someone has ever studied the following operator in the context of quantum mechanics: $$Q : L^2(\mathbb{R}) \to L^2(\mathbb{R})$$ $$(Q f)(x) := s(x) f(x),$$ where $s(x)$ is the ...
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### Quantization of a classical system (e.g. the case of a billard)

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) quantum mechanics, ...
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### Mathematical “proof” of the stability of atoms?

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 "solar system" model ...
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### Intuitive meaning of Double Commutant Theorem

Is there any intuitive explanation of the Double Commutant Theorem for Von Neumann Algebras? By intuitive I mean in terms of Quantum Mechanics. For example, duality of states and observables in the ...
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### Beginner question on constraints of a wave function in quantum mechanics

I am working through Griffiths’ Introduction to Quantum Mechanics. In chapter 1, he attempts to impose a condition such that $$\frac{d}{dt}\int_{-\infty}^\infty\left|\psi(x,t)\right|^2dx=0$$ so that ...
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### A novice question on Quantum Mechanics

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 corresponding to a ...
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### Interpretation of a parameter in forming a pseudodifferential operator

In Zworski's Semiclassical Analysis, he defines the following method of quantization: for a symbol $a = a(x,\xi) \in \mathscr{S}(\mathbb{R}^{2n})$ and $u \in \mathscr{S}(\mathbb{R}^n)$,  Op_t(a)u(x)...
In Hamiltonian mechanics, one essentially work with $\mathbb{R}^{2n}$. However, this is only a local description of our configuration manifold $M$. More precisely, the mechanical system is regarded as ...