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arXiv · 2406.06989

Regularized quantum motion in a bounded set: Hilbertian aspects

Fabio Bagarello·Jean-Pierre Gazeau·Camillo Trapani
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Abstract

It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous set of self-adjoint extensions. We prove that essential self-adjointness can be recovered by symmetrically weighting the momentum operator with a positive bounded function approximating the indicator function of the considered interval. This weighted momentum operator is consistently obtained from a similarly weighted classical momentum through the so-called Weyl-Heisenberg covariant integral quantization of functions or distributions.

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Fabio Bagarello, Jean-Pierre Gazeau, Camillo Trapani. 2024-06-11. Regularized quantum motion in a bounded set: Hilbertian aspects. https://arxiv.org/abs/2406.06989

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