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arXiv · 2308.13834

On the {\eta} pseudo PT symmetry theory for non-Hermitian Hamiltonians: time-dependent systems

Mustapha Maamache
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Abstract

In the context of non-Hermitian quantum mechanics, many systems are known to possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related to its adjoint H^{{\dag}} via the relation, H^{{\dag}}=PTHPT . We propose a derivation of pseudo PT symmetry and {\eta} -pseudo-Hermiticity simultaneously for the time dependent non-Hermitian Hamiltonians by intoducing a new metric {\eta}(t)=PT{\eta}(t) that not satisfy the time-dependent quasi-Hermiticity relation but obeys the Heisenberg evolution equation. Here, we solve the SU(1,1) time-dependent non-Hermitian Hamiltonian and we construct a time-dependent solutions by employing this new metric and discuss a concrete physical applications of our results.

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Mustapha Maamache. 2023-08-26. On the {\eta} pseudo PT symmetry theory for non-Hermitian Hamiltonians: time-dependent systems. https://arxiv.org/abs/2308.13834

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