EN
In this paper, we use some well-known techniques
of Supersymmetric QuantumMechanics (SUSYQM)
namely the factorization method and shape invariance,
to generate new analytically solvable potentials from
some interacting fermionic models in nonrelativistic limits.
These systems are described by the ordinary and the
harmonically trapped Schrödinger-Pauli particle models
and the Dirac-Coulomb Hamiltonian, this latter being set
in its nonrelativistic limits. The spectrum for each of these
models is obtained in a simple and transparent way. We
then generate new solvable potentials that describe interactions
between electromagnetic field and matter, paying
due attention to the subtleties inherent in the application
of SUSY to higher dimensional problems. SUSY breaking
problems related to the partner singularities are dicussed
along with the paper.