A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation

This study aims to apply a semi-classical approach using some analytically solvable potential functions accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. also at comparing accuracy within framework approximation. The performance approximation was investigated as function mass. In this approximation, nuclei were assumed move classical potential. Bohr-Sommerfeld quantization rule then applied calculate molecules numerically. results indicated that transition frequencies (v1ß0) all consistent with experimental ones, minimum percentage error 0.02% for ditritium (T2) molecule Modified-Rosen-Morse It demonstrated that, general, Rosen-Morse better terms calculating than Morse Interestingly, found be Manning-Rosen Finally, perform heavier potentials study.