The Physical Interpretation of PT-invariant Potentials

Abstract

A purely imaginary potential can provide a phenomenological description of creation and absorption of quantum mechanical particles. PT-invariance of such a potential ensures that the non-unitary phenomena occur in a balanced manner. In spite of wells and sinks which locally violate the conservation of quantum probability, there is no net get loss or gain of particles. This, in turn, is intuitively consistent with real energy eigenvalues.

4 pages

References in corpus (8)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Exact PT-Symmetry Is Equivalent to Hermiticity
• Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices
• Handedness of complex PT-symmetric potential barriers
• Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• Consistent relativistic Quantum Theory for systems/particles described by non-Hermitian Hamiltonians and Lagrangians
• Canonical Expansion of PT-Symmetric Operators and Perturbation Theory

Cited by in corpus (7)

• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Scattering in PT-symmetric quantum mechanics
• Solvability and PT-symmetry in a double-well model with point interactions
• Coupled-channel version of PT-symmetric square well
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems