Quantum Hamilton - Jacobi study of wave functions and energy spectrum of solvable and quasi - exactly solvable models

Abstract

In this thesis, the quantum Hamilton Jacobi (QHJ) formalism is used to study various exactly solvable (ES) and quasi -exactly solvable (QES) models. Using this method, we obtain the bound state eigenvalues and the eigenfunctions for the models studied. The central entity of this formalism in the logarithmic derivative of the wave function, known as the quantum momentum function (QMF).It is assumed that the point at infinity is an isolated singular point.The kowledge of the singularity structure of the QMF is used to arrive at the required solutions. We show that there are marked differences between the singularity structures of the ES and QES models.