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arXiv · 2308.13619

A new symmetry theory for non-Hermitian Hamiltonians

Mustapha Maamache·Nour El Houda Absi
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Abstract

The η pseudo PT symmetry theory, denoted by the symbol η, explores the conditions under which non-Hermitian Hamiltonians can possess real spectra despite the violation of PT symmetry, that is the adjoint of H, denoted H^{†} is expressed as H^{†}=PTHPT. This theory introduces a new symmetry operator, η=PTη, which acts on the Hilbert space. The η pseudo PT symmetry condition requires the Hamiltonian to commute with the η operator, leading to real eigenvalues. We discuss some general implications of our results for the coupled non hermitian harmonic oscillator.

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Mustapha Maamache, Nour El Houda Absi. 2024-01-06. A new symmetry theory for non-Hermitian Hamiltonians. https://arxiv.org/abs/2308.13619

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