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arXiv · 1905.00228

Stability of good quantum numbers in ground states

Tadahiro Miyao
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Abstract

Let $H$ be a self-adjoint operator, bounded from below and let $O$ be a bounded self-adjoint operator with purely discrete spectrum. Suppose that (i) $E(H)=\inf \mathrm{spec}(H)$ is a simple eigenvalue, and (ii) $H$ strongly commutes with $O$. Let $ψ_H$ be the eigenvector associated with $E(H)$. By the assumptions (i) and (ii), $ψ_H$ is an eigenvector of $O$: $Oψ_H=μ(H)ψ_H$. In the context of quantum mechanics, $μ(H)$ is called a good quantum number. In this note, we examine the stability of $μ(H)$ under perturbations of $H$ from a viewpoint of the order theory.

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Tadahiro Miyao. 2019-10-30. Stability of good quantum numbers in ground states. https://arxiv.org/abs/1905.00228

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