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arXiv · 2112.13535

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

F. Kecita·A. Bounames·M. Maamache
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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 $\mathcal{PT}$-symmetric one. Consequently, the solution of time-dependent Schrödinger 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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F. Kecita, A. Bounames, M. Maamache. 2021-12-27. A real expectation value of the time-dependent non-Hermitian Hamiltonians. https://doi.org/10.1088/1402-4896%2Fac3dbd

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