Exactly Solvable Hydrogen-like Potentials and Factorization Method

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

Coherent states for Hamiltonians generated by supersymmetry

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Poeschl-Teller potentials.Comment: LaTeX file, 26 pages, 3 eps figure

Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra

It is shown that the radial part of the Hydrogen Hamiltonian factorizes as the product of two not mutually adjoint first order differential operators plus a complex constant epsilon. The 1-susy approach is used to construct non-hermitian Hamiltonians with hydrogen spectra. Other non-hermitian Hamiltonians are shown to admit an extra `complex energy' at epsilon. New self-adjoint hydrogen-like Hamiltonians are also derived by using a 2-susy transformation with complex conjugate pairs epsilon, (c.c) epsilon.Comment: LaTeX2e file, 13 pages, 6 EPS figures. New references added. The present is a reorganized and simplified versio

The Phenomenon of Darboux Displacements

For a class of Schrodinger Hamiltonians the supersymmetry transformations can degenerate to simple coordinate displacements. We examine this phenomenon and show that it distinguishes the Weierstrass potentials including the one-soliton wells and periodic Lame functions. A supersymmetric sense of the addition formula for the Weierstrass functions is elucidated.Comment: 11 pages, latex, 2 eps figure

Nonlocal supersymmetric deformations of periodic potentials

Irreducible second-order Darboux transformations are applied to the periodic Schrodinger's operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials with periodicity defects and bound states embedded into the spectral gaps. The method is applied to the Lame and periodic piece-wise transparent potentials. An interesting phenomenon of translational Darboux invariance reveals nonlocal aspects of the supersymmetric deformations.Comment: 15 pages, latex, 9 postscript figure

SU(1,1) Coherent States For Position-Dependent Mass Singular Oscillators

The Schroedinger equation for position-dependent mass singular oscillators is solved by means of the factorization method and point transformations. These systems share their spectrum with the conventional singular oscillator. Ladder operators are constructed to close the su(1,1) Lie algebra and the involved point transformations are shown to preserve the structure of the Barut-Girardello and Perelomov coherent states.Comment: 11 pages, 5 figures. This shortened version (includes new references) has been adapted for its publication in International Journal of Theoretical Physic