A real expectation value of the time-dependent non-Hermitian Hamiltonians

Abstract

With the aim to solve the time-dependent Schrödinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent $\mathcal{P}\mathcal{T}$-symmetric one. Consequently, the solution of time-dependent Schrödinger equation becomes easily deduced and the evolution preserves the $\mathcal{C}(t)\mathcal{P}\mathcal{T}$-inner product, where $\mathcal{C}(t)$ is a obtained from the charge conjugation operator $\mathcal{C}$ through a time dependent unitary transformation. Moreover, the expectation value of the non-Hermitian Hamiltonian in the $\mathcal{C}(t)\mathcal{P}\mathcal{T}$ normed states is guaranteed to be real. As an illustration, we present a specific quantum system given by a quantum oscillator with time-dependent mass subjected to a driving linear complex time-dependent potential.

12 pages

References in corpus (7)

• Time-dependent version of cryptohermitian quantum theory
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Time evolution of non-Hermitian Hamiltonian systems
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians
• Adiabatic time-dependent metrics in PT-symmetric quantum theories
• Gauge linked time-dependent non-Hermitian Hamiltonians

Cited by in corpus (2)

• Exact solutions for time-dependent complex symmetric potential well
• Uncertainty Relation for Pseudo-Hermitian Quantum Systems