Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials

TL;DR

This paper investigates the algebraic structures of shift operators in one-dimensional exactly solvable quantum potentials, introducing a diagonalization method to construct SU(2) and SU(1,1) algebraic operators, and extends the approach to radial problems.

Contribution

It presents a novel diagonalization technique for constructing SU(2) and SU(1,1) algebra operators in exactly solvable potentials and applies the method to radial problems.

Findings

Constructed SU(2) and SU(1,1) operators for specific potentials

Established a method for operator construction via diagonalization

Extended the approach to radial quantum problems

Abstract

We mainly explore the linear algebraic structure like SU(2) or SU(1,1) of the shift operators for some one-dimensional exactly solvable potentials in this paper. During such process, a set of method based on original diagonalizing technique is presented to construct those suitable operator elements, J0, J_\pm that satisfy SU(2) or SU(1,1) algebra. At last, the similarity between radial problem and one-dimensional potentials encourages us to deal with the radial problem in the same way.