Regularized quantum motion in a bounded set: Hilbertian aspects

• URL: http://arxiv.org/abs/2406.06989v1
• Date: Tue, 11 Jun 2024 06:39:13 GMT
• Title: Regularized quantum motion in a bounded set: Hilbertian aspects
• Authors: Fabio Bagarello, Jean-Pierre Gazeau, Camillo Trapani,
• Abstract summary: We prove that essential self-adjointness can be recovered by symmetrically weighting the momentum operator with a positive bounded function. This weighted momentum operator is consistently obtained from a similarly weighted classical momentum.
• Score: 0.16385815610837165
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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