1. Regularized quantum motion in a bounded set: Hilbertian aspects
- Author
-
Bagarello, Fabio, Gazeau, Jean-Pierre, and Trapani, Camillo
- Subjects
Mathematical Physics ,Quantum Physics - 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., Comment: in press in Journal of Mathematical Analysis and Applications
- Published
- 2024