Effective particles in a multishell nanostructure with hardcore

In-medium effective carriers with position-dependent mass in a multishell heterostructure are analytically studied. We obtain the exact spectrum of three-dimensional bound eigenstates and the scattering wave-functions for several von Roos ordering classes. Ascribing a continuously varying mass to the carriers in a multilayer type spherical system we use our solutions to compute optical properties such as the absorption coefficients and refraction indices of a nanometric heterostructure. We analyze in detail the case of a GaAs/Al-GaAs alloy and show how these results depend on the ordering class of the kinetic Hamiltonian.