PT symmetric square well

Abstract

In a PT symmetrically complexified square well, bound states are constructed by the matching technique. Their energies prove real in a domain of weak non-Hermiticity, and continuous in the Hermitian limit. At a sequence of certain strong-Hermiticity thresholds, the lowest two energies merge and disappear.

9 pages, latex, one figure

Cited by in corpus (81)

• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Visualization of Branch Points in PT-Symmetric Waveguides
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Pseudospectra in non-Hermitian quantum mechanics
• Nonlinear reversal of PT symmetric phase transition in a system of coupled semiconductor micro-ring resonators
• Exceptional Point Dynamics in Photonic Honeycomb Lattices with PT Symmetry
• Scattering in PT-symmetric quantum mechanics
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Light transport in PT-invariant photonic structures with hidden symmetries
• Supersymetric laser arrays
• Spontaneous breakdown of PT symmetry in the solvable square-well model
• PT-symmetric square well and the associated SUSY hierarchies
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• Calculation of the Hidden Symmetry Operator for a $\cP\cT$-Symmetric Square Well
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• A return to observability near exceptional points in a schematic PT-symmetric model
• Application of Pseudo-Hermitian Quantum Mechanics to a PT-Symmetric Hamiltonian with a Continuum of Scattering States
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Solvability and PT-symmetry in a double-well model with point interactions
• Fragile PT-symmetry in a solvable model
• Coupled-channel version of PT-symmetric square well
• A Positive-Definite Scalar Product for Free Proca Particle
• Non-Hermitian interferometer: Unidirectional amplification without distortion
• Numerical calculation of the complex berry phase in non-Hermitian systems
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• Should PT symmetric quantum mechanics be interpreted as nonlinear?
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Matching method and exact solvability of discrete PT-symmetric square wells
• Mode pairs in $\mathcal{P}\mathcal{T}$-symmetric multimode waveguides
• Non-Hermitian spectral effects in a PT-symmetric waveguide
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Propagation of Electromagnetic Waves in Linear Media and Pseudo-Hermiticity
• Quantum toboggans
• Discrete quantum square well of the first kind
• Exactly solvable models with PT-symmetry and with an asymmetric coupling of channels
• Interlace properties for the real and imaginary parts of the wave functions of complex-valued potentials with real spectrum
• PT-symmetric supersymmetry in a solvable short-range model
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• Overcritical PT-symmetric square well potential in the Dirac equation
• Detecting Broken PT-Symmetry
• Strengthened PT-symmetry with P $\ne$ P${}^{†}$
• Quantum transport in non-Hermitian impurity array
• Periodic square-well potential and spontaneous breakdown of PT-symmetry
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• How to Test for Diagonalizability: The Discretized PT-Invariant Square-Well Potential
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Integrable nonlinear parity-time symmetric optical oscillator
• A new solvable complex PT-symmetric potential
• Parity-time symmetry under magnetic flux
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Infinite quantum well: a coherent state approach
• Non-Hermitian Hamiltonians and similarity transformations
• Absence of Floquet scattering in oscillating non-Hermitian potential wells
• Symmetrized exponential oscillator
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Hermitian - non-Hermitian interfaces in quantum theory
• Superoscillatory PT-symmetric potentials
• Quantum control and the challenge of non-Hermitian model-building
• Quantized Area of the Schwarzschild Black Hole: A non-Hermitian Perspective
• CPT-symmetric discrete square well
• Quantum square well with logarithmic central spike
• Real discrete spectrum of complex PT-symmetric scattering potentials
• Spectral inversion of an indefinite Sturm-Liouville problem due to Richardson
• "Striped" Rectangular Rigid Box with Hermitian and non-Hermitian $\mathcal{P}\mathcal{T}$ Symmetric Potentials
• PT-symmetry enabled stable modes in multi-core fiber
• Quantum probes for quantum wells
• Planarizable Supersymmetric Quantum Toboggans