Unified derivation of exact solutions for a class of quasi-exactly solvable models

Details Unified derivation of exact solutions for a class of quasi-exactly solvable models Unified derivation of exact solutions for a class of quasi-exactly solvable models

2011-11-04

arxiv.org/abs/1111.1050v2

Physics

Mathematical Physics

Latex file, 14 pages, many modifications made and misprints corrected

Scientific paper

We present a unified treatment of exact solutions for a class of four quantum mechanical models, namely the singular anharmonic potential, the generalized quantum isotonic oscillator, the soft-core Coulomb potential, and the non-polynomially modified oscillator. We show that all four cases are reducible to the same basic ordinary differential equation, which is quasi-exactly solvable. A systematic and closed form solution to the basic equation is obtained via the Bethe ansatz method. Using the result, general exact expressions for the energies and the allowed potential parameters are given explicitly for each of the four cases in terms of the roots of a set of algebraic equations. A hidden $sl(2)$ algebraic structure is also discovered in these models.

Affiliated with

Also associated with

No associations

Rating

Unified derivation of exact solutions for a class of quasi-exactly solvable models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unified derivation of exact solutions for a class of quasi-exactly solvable models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unified derivation of exact solutions for a class of quasi-exactly solvable models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-100583