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Second order supersymmetric approach is taken to the system describing motionof a quantum particle in a potential endowed with position-dependent effectivemass. It is shown that the intertwining relations between second order partnerHamiltonians may be exploited to obtain a simple shape-invariant condition.Indeed a novel relation between potential and mass functions is derived, whichleads to a class of exactly solvable model. As an illustration of ourprocedure, two examples are given for which one obtains whole spectraalgebraically. Both shape-invariant potentials exhibit harmonic-oscillator-likeor singular-oscillator-like spectra depending on the values of theshape-invariant parameter.

Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry