Creation and annihilation operators and coherent states for the PT-symmetric oscillator

Abstract

We construct two commuting sets of creation and annihilation operators for the PT-symmetric oscillator. We then build coherent states of the latter as eigenstates of such annihilation operators by employing a modified version of the normalization integral that is relevant to PT-symmetric systems. We show that the coherent states are normalizable only in the range (0, 1) of the underlying coupling parameter $\alpha$.

one additional reference, final version to be published in MPLA

References in corpus (4)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
• Space of State Vectors in PT Symmetrical Quantum Mechanics
• Annihilation and creation operators in non-Hermitian supersymmetric quantum mechanics

Cited by in corpus (10)

• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
• Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
• Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
• Pseudo-bosons, so far
• Coherent states of non-Hermitian quantum systems
• A pedestrian introduction to coherent and squeezed states
• Constraining four neutrino mass patterns from neutrinoless double beta decay
• Generalized Grassmannian Coherent States For Pseudo-Hermitian $n$ Level Systems
• Two dimensional non-Hermitian harmonic oscillator: coherent states