Quasi-Exactly Solvable Potentials with Three Known Eigenstates

Abstract

We propose a new SUSY method for construction of the quasi-exactly solvable (QES) potentials with three known eigenstates. New QES potentials and corresponding energy levels and wave functions of the ground state and two lowest excited state are obtained. The proposed scheme allows also to construct families of exactly solvable non-singular potentials which are SUSY partners of the well-known ones.

15 pages, LaTeX, no figures, revised version

References in corpus (6)

• Quasi-exactly solvable quartic potential
• Conditionally exactly solvable potentials: A supersymmetric construction method
• Quasi-Exactly Solvable Potentials with Two Known Eigenstates
• Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?
• Zero-energy states for a class of quasi-exactly solvable rational potentials
• Quasi-exactly Solvable Lie Superalgebras of Differential Operators

Cited by in corpus (7)

• SUSY Intertwining Relations of Third Order in Derivatives
• On one-dimensional Schroedinger problems allowing polynomial solutions
• Deformed shape invariance symmetry and potentials in curved space with two known eigenstates
• A General Approach of Quasi-Exactly Solvable Schroedinger Equations
• A General Approach of Quasi-Exactly Solvable Schroedinger Equations with Three Known Eigenstates
• Supersymmetric approach for generating quasi-exactly solvable potentials with arbitrary two known eigenstates
• Entangled states in supersymmetric quantum mechanics