Two dimensional non-Hermitian harmonic oscillator: coherent states
arXiv:2012.04526 · doi:10.1088/1402-4896/ab240b
Abstract
In this study, we introduce a two dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time independent Schrödinger equation yields real eigenvalues with complex eigenfunctions. We also construct the coherent state of the system by using a superposition of 12 eigenfunctions. Using the complex correspondence principle for the probability density we investigate the possible modifications in the probability densities due to the non-Hermitian aspect of the Hamiltonian.
arXiv comment11 pages and 5 figures
References in corpus (47)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
- Complex Extension of Quantum Mechanics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- PT-Symmetric Quantum Mechanics
- Loss-induced suppression and revival of lasing
- Pseudo-Hermitian Representation of Quantum Mechanics
- Experimental Study of Active LRC Circuits with PT-Symmetries
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- PT-Symmetric Phonon Laser
- Reversing the Pump-Dependence of a Laser at an Exceptional Point
- Introduction to PT-Symmetric Quantum Theory
- Exact PT-Symmetry Is Equivalent to Hermiticity
- Must a Hamiltonian be Hermitian?
- PT -symmetric harmonic oscillators
- Observation of Defect States in PT-Symmetric Optical Lattices
- Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
- Quasi-exactly solvable quartic potential
- sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
- PT-Symmetric Wave Chaos
- PT-symmetric scattering in flow duct acoustics
- A family of complex potentials with real spectrum
- Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
- Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
- Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
- Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
- Jarzynski equality in -symmetric quantum mechanics
- The Coulomb - harmonic oscillator correspondence in PT-symmetric quantum mechanics
- Complex Correspondence Principle
- Scattering by finite periodic -symmetric structures
- Finite-Dimensional PT-Symmetric Hamiltonians
- PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
- PT Symmetry as a Generalization of Hermiticity
- All Hermitian Hamiltonians Have Parity
- Should PT symmetric quantum mechanics be interpreted as nonlinear?
- Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
- Creation and annihilation operators and coherent states for the PT-symmetric oscillator
- Thermodynamics of Quantum Heat Bath
- Dynamical evolutions in non-Hermitian triple-well system with complex potential
- Coherent states of non-Hermitian quantum systems
- Exactly solvable -symmetric models in two dimensions
- Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type
- Coherent state of the effective mass harmonic oscillator
- Non-Hermitian Hamiltonian versus E=0 localized states
- Solvable PT symmetric Hamiltonians