Exactly Solvable Hydrogen-like Potentials and Factorization Method

Details Exactly Solvable Hydrogen-like Potentials and Factorization Method Exactly Solvable Hydrogen-like Potentials and Factorization Method

1998-06-05

arxiv.org/abs/quant-ph/9806020v3

J.Phys.A31:10163-10179,1998

Physics

Quantum Physics

LaTex file, 21 pages, 2 PostScript figures and some references added. To be published in J. Phys. A: Math. Gen. (1998)

Scientific paper

10.1088/0305-4470/31/50/012

A set of factorization energies is introduced, giving rise to a generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian. An algebraic intertwining technique involving such factorization energies leads to derive $n$-parametric families of potentials in general 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.

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