Investigation of Heisenberg algebra for a modified anti-de Sitter and modified anti-Snyder models

Abstract

In this paper, we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle. For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem. Also, we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle. Then, we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified (anti)-de Sitter and (anti)-Snyder models in both position and in the momentum space.