Generalized Uncertainty Principle and Self-Adjoint Operators
  In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators 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. 
Venkat Balasubramanian, Saurya Das, Elias C. Vagenas
hep-th gr-qc hep-ph quant-ph