PT-symmetric quartic anharmonic oscillator and position-dependent mass in a perturbative approach

Abstract

To lowest order of perturbation theory we show that an equivalence can be established between a $\mathcal{P}\mathcal{T}$-symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian $h$. An important feature of $h$ is that it reveals a domain of couplings where the quartic potential could be attractive, vanishing or repulsive. We also determine the associated physical quantities.

8 pages, no figure, to appear in special issue of Czech. J. Phys

References in corpus (12)

• Introduction to PT-Symmetric Quantum Theory
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Quasi-exactly solvable quartic potential
• On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
• PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
• Pseudo-Hermiticity and some consequences of a generalized quantum condition
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
• Real Description of Classical Hamiltonian Dynamics Generated by a Complex Potential
• Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework
• A Perturbative Treatment Of A Generalized PT-Symmetric Quartic Anharmonic Oscillator
• Semiclassical analysis of a complex quartic Hamiltonian
• Quasi-exact minus-quartic oscillators in strong-core regime

Cited by in corpus (6)

• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Approximate Analytical Solutions of the Klein-Gordon Equation for Hulthen Potential with Position-Dependent Mass
• Position-dependent mass, finite-gap systems, and supersymmetry
• Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
• Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass
• A squeeze-like operator approach to position-dependent mass in quantum mechanics