Novel quasi-exactly solvable models with anharmonic singular potentials

Abstract

We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly via the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of a set of algebraic equations.

LaTex 18 pages. Updated version to appear in Annals of Physics

References in corpus (3)

• Exact polynomial solutions of second order differential equations and their applications
• Asymptotic Iteration method for singular potentials
• Unified derivation of exact solutions for a class of quasi-exactly solvable models

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• On Some Quantum Correction to the Coulomb Potential in Generalized Uncertainty Principle Approach
• Perturbation-based Non-perturbative Method
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