Exact Solutions of Schrödinger Equation, Thermodynamic Properties and Expectation values of Pseudoharmonic Oscillator in de Sitter and Anti de Sitter spacetime

Abstract

In this work, the radial Schrödinger equation with pseudoharmonic oscillator is first expressed in both de Sitter and Anti de Sitter spaces time using the Extended Uncertainty Principle (EUP) formalism. The eigensolutions of the Schrödinger equation is obtained in exact form using the Nikiforov-Uvarov functional analysis (NUFA) method. The effects of quantum numbers and spatial deformation parameter on the eigensolutions obtained are studied in both spaces. In addition, the graphical variations of both thermodynamic properties and expectation values with temperature parameter and quantum numbers, respectively, have been discussed for varying deformation parameters. The energy eigenvalues increase with increase in the spatial deformation parameter in Anti de Sitter (AdS) spacetime and there is an energy decrease in de Sitter (dS) spacetime, as deformation parameter increases. The variations observed for thermodynamic properties and expectation values with temperature and quantum number, respectively in dS spacetime are inversely related to that observed in AdS spacetime.