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On quantum integrability and Hamiltonians with pure point spectrum

A. Enciso·D. Peralta-Salas
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Abstract

We prove that any $n$-dimensional Hamiltonian operator with pure point spectrum is completely integrable via self-adjoint first integrals. Furthermore, we establish that given any closed set $Σ\subset\mathbb R$ there exists an integrable $n$-dimensional Hamiltonian which realizes it as its spectrum. We develop several applications of these results and discuss their implications in the general framework of quantum integrability.

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A. Enciso, D. Peralta-Salas. 2004-07-06. On quantum integrability and Hamiltonians with pure point spectrum. https://arxiv.org/abs/math-ph/0406022

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