Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics

Abstract

The continuity equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The normalization condition of eigenfunctions is modified in accordance with this new conservation law and illustrated with some detailed examples.

16 pages, amssym

Cited by in corpus (76)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear modes in finite-dimensional PT-symmetric systems
• Time evolution of non-Hermitian Hamiltonian systems
• Space of State Vectors in PT Symmetrical Quantum Mechanics
• Scattering in PT-symmetric quantum mechanics
• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
• Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials
• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• Completeness and Orthonormality in PT-symmetric Quantum Systems
• Scattering theory with localized non-Hermiticities
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Spontaneous breakdown of PT symmetry in the solvable square-well model
• Handedness of complex PT-symmetric potential barriers
• PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential
• Pseudo-Hermiticity, weak pseudo-Hermiticity and eta-orthogonality condition
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• PT-symmetric square well and the associated SUSY hierarchies
• Discrete PT-symmetric models of scattering
• An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners
• Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthen Potential by the Nikiforov-Uvarov Method
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Exact quantization of a PT-symmetric (reversible) Liénard-type nonlinear oscillator
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• PT symmetry of a conditionally exactly solvable potential
• Solvability and PT-symmetry in a double-well model with point interactions
• Isospectral Hamiltonians from Moyal products
• Parametric instability of non-Hermitian systems near the exceptional point
• Coupled-channel version of PT-symmetric square well
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• A new class of non-Hermitian Hamiltonians with real spectra
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• P,T,PT, and CPT invariance of Hermitian Hamiltonians
• An exactly solvable PT symmetric potential from the Natanzon class
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
• Pseudo-Hermitian approach to energy-dependent Klein-Gordon models
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• PT-Symmetric Quantum Theory Defined in a Krein Space
• PT-symmetry and its spontaneous breakdown explained by anti-linearity
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Matching method and exact solvability of discrete PT-symmetric square wells
• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Creation and annihilation operators and coherent states for the PT-symmetric oscillator
• Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• Remarks on PT-pseudo-norm in PT-symmetric quantum mechanics
• 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
• A pedestrian introduction to coherent and squeezed states
• Investigation of PT-symmetric Hamiltonian systems from an alternative point of view
• A black potential for spin less particles
• Conserved Correlation in PT -symmetric Systems: Scattering and Bound States
• Accidental crossings of eigenvalues in one-dimensional complex PT-symmetric Scarf-II potential
• Linear representation of energy-dependent Hamiltonians
• A new solvable complex PT-symmetric potential
• No-signaling principle and Bell inequality in PT-symmetric quantum mechanics
• Pseudo-reality and pseudo-adjointness of Hamiltonians
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• PT-symmetric non-polynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV
• Generalized continuity equations from two-field Schrödinger Lagrangians
• An ansatz for the eigenstates in PT-symmetric quantum mechanics
• Supersymmetric approach to exact solutions of $(1+1)$-dimensional time-independent Klein-Gordon equation : Application to a position-dependent mass and a $\mathcal{P}\mathcal{T}$-symmetric vector potential
• Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential
• Classification of the conditionally observable spectra exhibiting central symmetry
• Real discrete spectrum of complex PT-symmetric scattering potentials
• Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity