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.

arXiv comment11 pages

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Cited by in corpus (3)

• Inhomogeneous modes in the PT-symmetric quantum cosmology
• 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