PT-Symmetric Quantum Mechanics: A Precise and Consistent Formulation

Abstract

The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical equivalence of PT-symmetric and conventional quantum mechanics. The results reported in this paper apply to arbitrary PT-symmetric Hamiltonians with a real and discrete spectrum. They hold regardless of whether the boundary conditions defining the spectrum of the Hamiltonian are given on the real line or a complex contour.

9 pages, to appear in Czech. J. Phys

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• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Scattering in PT-symmetric quantum mechanics
• Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
• Delta-Function Potential with a Complex Coupling
• Parity-time symmetry in optical microcavity systems
• Energy Observable for a Quantum System with a Dynamical Hilbert Space and a Global Geometric Extension of Quantum Theory
• A return to observability near exceptional points in a schematic PT-symmetric model
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Spectral Singularities of a General Point Interaction
• Solvability and PT-symmetry in a double-well model with point interactions
• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• PT-symmetric supersymmetry in a solvable short-range model
• Entanglement in Non-Hermitian Quantum Theory
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Lower bound of minimal time evolution in quantum mechanics
• An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems
• Quasi-exact minus-quartic oscillators in strong-core regime
• Consistent treatment of quantum systems with a time-dependent Hilbert space