Parameter Space of Morse Oscillator

TL;DR

This paper analyzes the mathematical structure and parameter space of the Morse oscillator, revealing how operator relations depend on system parameters and visualizing the parameter space to understand these dependencies.

Contribution

It provides a detailed analysis of the SU(2) group structure in the Morse oscillator and introduces a visualization of its parameter space, which is applicable to other quantum systems.

Findings

Operator commutation relations depend on Morse oscillator parameters

Parameter space visualization reveals structural changes in operators

Algorithm applicable to other quantum systems

Abstract

We present the analysis of mathematical structure of SU(2) group, specifically the commutation relation between raising and lowering operators of the Morse oscillator. The relationship between the commutator of operators and other parameters of Morse oscillator is investigated. We show that the mathematical structure of operators which depends on the parameters of Morse oscillator may change our conventional expectation. The parameter space of Morse oscillator is visualized to scrutinize the mathematical relations that are related to the Morse oscillator. This parameter space is the space of possible parameter values that depend on the depth of the Morse potential well and other parameters. The algorithm that we present is also applicable to other quantum systems with certain modifications.