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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