Ladder operators for the Ben Daniel-Duke Hamiltonians and their SUSY partners

Abstract

Position dependent mass systems can be described by a class of operators which include the Ben Daniel-Duke Hamiltonians. The usual methods to solve this kind of problems are, in general, either numerical or those looking for a connection with constant mass problems. In this paper we impose the existence of first-order ladder operators to fix our initial system. Then, we perform the first and second order supersymmetric transformations to generate families of Hamiltonians whose eigenfunctions are known analytically for a given mass profile.

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Cited by in corpus (7)

• On the position dependent effective mass Hamiltonian
• Generalized Uncertainty principle and momentum-dependent effective mass Schrodinger equation
• Isochronous oscillator with a singular position-dependent mass and its quantization
• Generalized Liénard systems and isochronous connections
• Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra
• Extended coupled SUSY, pseudo-bosons and weak squeezed states
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions