Exactly solvable hydrogen-like potentials and the factorization method

Abstract

A set of factorization energies is introduced, giving rise to a generalization of the Schrodinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian. An algebraic intertwining technique involving such factorization energies leads us to derive n-parametric families of potentials which, in general, are almost-isospectral to the hydrogen-like radial Hamiltonians. The construction of SUSY partner Hamiltonians with ground state energies greater than the corresponding ground state energy of the initial Hamiltonian is also explicitly performed.