Spectroscopic Studies of Some Diatomic Molecules using Spectrum Generating Algebra Approach

TL;DR

This paper solves the 3D Schrödinger equation for diatomic molecules using Spectrum Generating Algebra, providing explicit energies, eigenfunctions, and expectation values, confirming the Heisenberg Uncertainty Principle across various molecules.

Contribution

It introduces an algebraic method to obtain bound states and expectation values for diatomic molecules with arbitrary quantum numbers, extending previous approaches.

Findings

Explicit bound state energies and eigenfunctions derived.

Closed-form matrix elements for r^2 and r d/dr obtained.

Heisenberg Uncertainty Principle verified for all molecules.

Abstract

For arbitrary values n and l quantum numbers, we present the solutions of the 3-dimensional Schrodinger wave equation with the pseudoharmonic potential via SU(1,1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The matrix elements r2 and r d/dr are obtained (in a closed form) directly from the creation and annihilation operators. In addition, the expectation values of r2 and p2 and the Heisenberg Uncertainty Products (HUP) for set of diatomic molecules (O2, I2, N2, H2, CO, NO, HCl, CH, LiH, ScH, TiH, VH, CrH, MnH, TiC, NiC, ScN, ScF, Ar2) for arbitrary values of n and l quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature. It is also shown that the HUP is obeyed for all diatomic molecules considered.