The su(1,1) dynamical algebra from the Schr\"odinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator

TL;DR

This paper constructs ladder operators for various N-dimensional quantum systems using Schrödinger factorization, revealing that their dynamical algebra is the su(1,1) Lie algebra, thus unifying their algebraic structure.

Contribution

It generalizes the construction of ladder operators for multiple N-dimensional systems and identifies the su(1,1) algebra as their underlying dynamical algebra.

Findings

Ladder operators are constructed for hydrogen, Mie-type, harmonic, and pseudo-harmonic oscillators.

The dynamical algebra for these systems is identified as su(1,1).

The approach applies to arbitrary dimensions.

Abstract

We apply the Schr\"odinger factorization to construct the ladder operators for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the $su(1,1)$ Lie algebra.