Methods for Generating Quasi-Exactly Solvable Potentials

Abstract

We describe three different methods for generating quasi-exactly solvable potentials, for which a finite number of eigenstates are analytically known. The three methods are respectively based on (i) a polynomial ansatz for wave functions; (ii) point canonical transformations; (iii) supersymmetric quantum mechanics. The methods are rather general and give considerably richer results than those available in the current literature.

12 pages, LaTex

References in corpus (1)

• Supersymmetry and Quantum Mechanics

Cited by in corpus (6)

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• Infinite families of position-dependent mass Schrödinger equations with known ground and first excited states
• Supersymmetric approach for generating quasi-exactly solvable potentials with arbitrary two known eigenstates