Quantum Evolution of the Time-Dependent Non-Hermitian Hamiltonians: Real Phases

Abstract

Explicitly time-dependent pseudo-Hermitian (TDPH) invariants theory systems, with a time-dependent (TD) metric, is developed for a time-dependent non Hermitian (TDNH) quantum systems. We derive a simple relation between the eigenstates of this pseudo-Hermitien (PH) invariant and the solutions of the Schrodinger equation. A physical system is treated in detail: the TD Swanson model, where an explicitly TDPH invariant is derived for this system, the eigenvalues and eigenstates of the invariant are calculated explicitly.

11 pages

References in corpus (4)

• Three-Hilbert-Space Formulation of Quantum Mechanics
• Adiabatic time-dependent metrics in PT-symmetric quantum theories
• Unitarity of the time-evolution and observability of non-Hermitian Hamiltonians for time-dependent Dyson maps
• Gauge linked time-dependent non-Hermitian Hamiltonians

Cited by in corpus (2)

• Time evolution of quantum systems with time-dependent non-Hermitian Hamiltonian and the pseudo Hermitian invariant operator
• Non-Unitary evolution of quantum time-dependent non-Hermitian systems