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

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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