Generalized Jaynes-Cummings Model and Shape Invariant Potentials: Master Function Approach

Abstract

In this work, we use the master function formalism and solve the generalized Jaynes-Cummings Hamiltonian for some solvable potentials. By using this approach, we apply the shape invariance properties of associated differential equations of mathematical physics with respect to secondary quantum number, and show that the two-component spinor wave function of system can be obtained by Rodrigues representation of orthogonal polynomials. The energy eigenvalue of system is also written in terms of the spectrum of solvable models given by master function approach.