The Quantum Effective Mass Hamilton-Jacobi Problem

TL;DR

This paper explores the quantum Hamilton-Jacobi theory with position-dependent mass, analyzing Morse and Pöschl-Teller potentials, and introduces methods to find eigenstates of non-Hermitian Hamiltonians without differential equations.

Contribution

It presents a novel approach using the residue method and Riccati equation to solve the quantum effective mass-Hamilton-Jacobi problem for specific potentials.

Findings

Solutions for quantum effective mass-Hamilton-Jacobi equations obtained

Eigenstates of non-Hermitian Hamiltonians derived without differential equations

Different singularity structures of mass functions analyzed

Abstract

In this article, the quantum Hamilton- Jacobi theory based on the position dependent mass model is studied. Two effective mass functions having different singularity structures are used to examine the Morse and Poschl- Teller potentials. The residue method is used to obtain the solutions of the quantum effective mass- Hamilton Jacobi equation. Further, it is shown that the eigenstates of the generalized non-Hermitian Swanson Hamiltonian for Morse and Poschl-Teller potentials can be obtained by using the Riccati equation without solving a differential equation.