Spectroscopic Studies of Some Diatomic Molecules using Spectrum Generating Algebra Approach

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.

K. J. Oyewumi, K. D. Sen · 2011