Quasi-exact Treatment of the Relativistic Generalized Isotonic Oscillator

Abstract

We investigate the pseudospin symmetry case of a spin-1/2 particle governed by the generalized isotonic oscillator, by presenting quasi exact polynomial solutions to Dirac equation with pseudospin symmetry vector and scalar potentials. The resulting equation is found to be quasi-exactly solvable owing to the existence of a hidden $sl(2)$ algebraic structure. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. Analytic expression for the energy is obtain and the wavefunction is derived in terms of the roots to a set of Bethe ansatz equations.

References in corpus (5)

• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Exact polynomial solutions of second order differential equations and their applications
• Unified derivation of exact solutions for a class of quasi-exactly solvable models
• The generalized quantum isotonic oscillator
• Generalized quantum isotonic nonlinear oscillator in d dimensions

Cited by in corpus (3)

• Quasi-exactly solvable relativistic soft-core Coulomb models
• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential