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Non-Hermitian time-dependent quantum systems with real energies

A. de Souza Dutra·M. B. Hott·V. G. C. S dos Santos
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Abstract

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum chemistry, which consists of an oscillator with time-dependent mass and frequency under the action of a time-dependent imaginary potential. The propagator for a general time-dependence of the parameters and the wave-functions are obtained explicitly for constant frequency and mass and a linear time-dependence in the potential. The wave-functions are used to obtain the expectation value of the Hamiltonian. Although it is neither Hermitian nor PT symmetric, the case under study exhibits real values of energy.

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A. de Souza Dutra, M. B. Hott, V. G. C. S dos Santos. 2004-09-16. Non-Hermitian time-dependent quantum systems with real energies. https://arxiv.org/abs/quant-ph/0311044

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