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

• URL: http://arxiv.org/abs/2112.13535v1
• Date: Mon, 27 Dec 2021 06:27:33 GMT
• Title: A real expectation value of the time-dependent non-Hermitian Hamiltonians
• Authors: F. Kecita, A. Bounames, M. Maamache
• Abstract summary: We solve the time-dependent Schr"odinger equation associated to a time-dependent non-Hermitian Hamiltonian. The expectation value of the non-Hermitian Hamiltonian in the $mathcalC(tmathcal)PT$ normed states is guaranteed to be real.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: With the aim to solve the time-dependent Schr\"{o}dinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent $\mathcal{PT}$-symmetric one. Consequently, the solution of time-dependent Schr\"{o}dinger equation becomes easily deduced and the evolution preserves the $\mathcal{C(}t\mathcal{)PT}$-inner product, where $\mathcal{C(}t\mathcal{)}$ 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 $\mathcal{C(}t\mathcal{)PT}$ 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.

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