Exactly solvable double-well potential in Schrodinger equation for inversion mode of phosphine molecule

The reduced mass of the effective quantum particle for the inversion mode.2 of phosphine molecule PH3 is known to be a position dependent one. In the present article the inversion spectrum of PH3 is considered with the help of the Schrodinger equation (SE) with position dependent mass and corresponding modified double-well potential. The SE is shown to be exactly solvable. The results are used for the analysis of the pertinent experimental data available in literature. We are based on the reliable value nu(2) = E-2-E-0 = 992.1 cm(-1) (2 nu(2) = E-4-E-0 = 1972.5 cm(-1); 3 nu(2) = E-6-E-0 = 2940.8 cm(-1); 4 nu(2) = E-8-E-0 = 3895.9 cm(-1)) obtained by.Spirko et al. Also we use the value for the barrier height E-b = 12300 cm(-1) that seems to be commonly accepted at present and the hypothetical value for the energy splitting of the 11-th doublet of the 10.2 band s(10) = E-21-E-20 approximate to 7.2 cm(-1) suggested in the literature. Definite predictions are derived for the energy splitting of the 4-th doublet of the 3 nu(2) band s(3) = E-7-E-6 that is a test one for the observation in the experiment of Okuda et al. SE with position dependent mass provides self-consistently the required values of {nu(2); E-b; s(10)} yielding s(3) = 6.21 center dot 10(-12) cm(-1).

Automated summary

This study focuses on the inversion spectrum of PH3 molecule using the Schrodinger equation with position dependent mass, showing that the SE is solvable and providing predictions for energy splitting values. Analysis of experimental data and reliable values from previous studies help validate the findings and provide new insights into the behavior of the molecule.