A General Approach of Quasi-Exactly Solvable Schroedinger Equations

Abstract

We construct a general algorithm generating the analytic eigenfunctions as well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians. Both exact and quasi-exact Hamiltonians enter our formalism but we focus on quasi-exact interactions for which no such general approach has been considered before. In particular we concentrate on a generalized sextic oscillator but also on the Lame and the screened Coulomb potentials.

23 pages, no figure

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Cited by in corpus (3)

• An extended class of L2-series solutions of the wave equation
• L2 series solutions of the Dirac equation for power-law potentials at rest mass energy
• A General Approach of Quasi-Exactly Solvable Schroedinger Equations with Three Known Eigenstates