(2015-12-16) Balasubramanian, Venkat; Das, Saurya; 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.