Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach

Abstract

Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second order linear differential operator with position depndent coefficients and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation (PCT) to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [14,18] for the particular case N = 1 and N = 2 respectively.

Some references have been added

References in corpus (4)

• Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schroedinger Hamiltonians
• N-fold Supersymmetry in Quantum Systems with Position-dependent Mass
• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry

Cited by in corpus (16)

• Nonlinear Dynamics of a position-dependent mass driven Duffing-type oscillator
• Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold Supersymmetry
• Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
• Bi-squeezed states arising from pseudo-bosons
• Generalized Heisenberg algebra and (non linear) pseudo-bosons
• The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass
• Appearances of pseudo-bosons from Black-Scholes equation
• Nonsingular potentials from excited state factorization of a quantum system with position dependent mass
• Non self-adjoint Hamiltonians with complex eigenvalues
• Supersymmetry Across Nanoscale Heterojunction
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Gibbs states defined by biorthogonal sequences
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations
• Comparison theorems for the position-dependent mass Schroedinger equation