Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

Abstract

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is applied to the Hermitian analogue of the PT-symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a PT-symmetric extension of the one-parameter trigonometric Poschl-Teller potential.

13 pages, no figure, modified presentation, 6 additional references, published version

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Cited by in corpus (16)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Delta-Function Potential with a Complex Coupling
• Position Dependent Mass Oscillators and Coherent States
• Morse potential and its relationship with the Coulomb in a position-dependent mass background
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
• Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
• Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics
• Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator
• Propagation of Electromagnetic Waves in Linear Media and Pseudo-Hermiticity
• A Family of Exactly Solvable Radial Quantum Systems on Space of Non-Constant Curvature with Accidental Degeneracy in the Spectrum
• Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass
• PT-symmetric quartic anharmonic oscillator and position-dependent mass in a perturbative approach
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity