Exact solutions of position-dependent mass Schrodinger equation with pseudoharmonic oscillator and its thermal properties using extended Nikiforov-Uvarov method

In this work, we find the exact solution of Schrodinger wave equation for position-dependent mass with pseudoharmonic oscillator using extended Nikiforov-Uvarov method. We obtained the energy eigen equation presented in a closed and compact form and used the result to study both superstatistics and thermodynamic properties by first determining the partition function of the system. The unnormalized wave function was obtained and expressed in terms of confluent Heun function. Using the resulting energy eigen equation, the numerical computation was computed for varying masses with fixed physical constant potential parameter lambda. The numerical result shows that the bound state energies increase with quantum states but decreases with the dependent mass m(x). The thermodynamics and superstatistics plots are also reported.