  The solving of the Schrodinger equation for a position-dependent mass quantum
system is studied in two ways. First, it is found the interaction which must be
applied on a mass m(x) in order to supply it with a particular spectrum of
energies. Second, given a specific potential V(x) acting on the mass m(x), the
related spectrum is found. The method of solution is applied to a wide class of
position-dependent mass oscillators and the corresponding coherent states are
constructed. The analytical expressions of such position-dependent mass
coherent states preserve the functional structure of the Glauber states.
