The Quantum Effective Mass Hamilton-Jacobi Problem

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.

References in corpus (16)

• Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions
• A singular position-dependent mass particle in an infinite potential well
• Probability and complex quantum trajectories
• Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
• Morse potential and its relationship with the Coulomb in a position-dependent mass background
• Generalized Swanson models and their solutions
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry and position-dependent mass models
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
• Scattering in the PT-symmetric Coulomb potential
• Pseudo supersymmetric partners for the generalized Swanson model
• Understanding chemical reactions within a generalized Hamilton-Jacobi framework
• Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Shape invariance and the exactness of quantum Hamilton-Jacobi formalism
• The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism

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• A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term
• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
• Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
• Dual wavefunctions in two-dimensional quantum mechanics
• Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton-Jacobi formalism
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• Quantum Hamilton-Jacobi Quantization and Shape Invariance