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arXiv · 2003.13424

Constraints on the choice of position dependent effective mass and external potential for the existence of Lewis-Riesenfeld invariance and quantum canonical transformation

Kalpana Biswas·Jyoti Prasad Saha·Pinaki Patra
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Abstract

Lewis-Riesenfeld -Ermakov's (LR) invariant method for the construction of time-dependent phase-space invariant is extended for the general quantum system with position-dependent effective mass (PDEM) Hamiltonian. It turns out that, only a specific class of PDEM and a particular class of external potentials will exhibit the LR-invariant operator in close form. Then we have determined a class of unitary time-dependent quantum canonical transformation for the concerned PDEM and external potentials so that an equivalent time-independent PDEM Hamiltonian is obtained.

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Kalpana Biswas, Jyoti Prasad Saha, Pinaki Patra. 2020-03-18. Constraints on the choice of position dependent effective mass and external potential for the existence of Lewis-Riesenfeld invariance and quantum canonical transformation. https://arxiv.org/abs/2003.13424

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