Generalized uncertainty principle and self-adjoint operators
Vagenas, Elias C.
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian oper- ators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Sherpa Romeo green journal. Permission to archive author manuscript.
Generalized uncertainty principle , GUP , Hamiltonian operators , Self-adjoint , Quantum gravity phenomenology , Quantum mechanics
Balasubramanian, V., Das, S., & Vagenas, E. C. (2015). Generalized uncertainty principle and self-adjoint operators. Annals of Physics, 360, 1-18. https://doi.org/10.1016/j.aop.2015.04.033