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arXiv · 2006.02843

$\mathcal{PT}$-Symmetric Generalized Extended Momentum Operator

M. Izadparast·S. Habib Mazharimousavi
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Abstract

We develop further the concept of generalized extended momentum operator (GEMO), which has been introduced very recently in \citep{M.H2}, and propose the so called $\mathcal{PT}$-symmetric GEMO. In analogy with GEMO, the $\mathcal{PT}$-symmetric GEMO also satisfies the extended uncertainty principle (EUP) relation. Moreover, the corresponding Hamiltonian that is constructed upon the $\mathcal{PT}$-symmetric GEMO, with a real or $\mathcal{PT}$-symmetric potential, remains non-Hermitian but $\mathcal{PT}$-symmetric and consequently its energy and momentum eigenvalues are real. We apply our formalism to a quasi-free quantum particle and the exact solutions for the energy spectrum are presented.

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M. Izadparast, S. Habib Mazharimousavi. 2020-06-04. $\mathcal{PT}$-Symmetric Generalized Extended Momentum Operator. https://doi.org/10.1088/1402-4896%2Fabb85c

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