We discuss the relationship between exact solvability of the Schrödinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the frame of supersymmetric quantum mechanics. The one-dimensional Schrödinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.
The eigenvalues of the potentials V 1 (r) = r 6 , and of the special cases of these potentials such as the Kratzer and Goldman-Krivchenkov potentials, are obtained in Ndimensional space. The explicit dependence of these potentials in higherdimensional space is discussed, which have not been previously covered.
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