Analytic description of inversion vibrational mode for ammonia molecule

Abstract

The one-dimensional Schrödinger equation with symmetric trigonometric double-well potential is exactly solved via angular prolate spheroidal function. Although it is inferior compared with multidimensional counterparts and its limitations are obvious nevertheless its solution is shown to be analytic rather than commonly used numerical or approximate semiclassical (WKB) one. This comprises the novelty and the merit of the present work. Our exact analytic description of the ground state splitting can well be a referee point for comparison of the accuracy of numerous WKB formulas suggested in the literature. The approach reasonably well suits for the inversion mode in the ammonia molecule $N{H}_3$ and thus yields a new theoretical tool for its description. The results obtained provide good quantitative description of relevant experimental data on microwave and IR spectroscopy of $N{H}_3$.

16 pages, 2 figures, Final version, misprint in Appendix 1 has been corrected

References in corpus (5)

• Magnetic quantum dots and rings in two dimensions
• Semi-classical formula for quantum tunneling in asymmetric double-well potentials
• Two-electron atom with a screened interaction
• Localization or tunneling in asymmetric double-well potentials
• Exact solution of Smoluchowski's equation for reorientational motion in Maier-Saupe potential

Cited by in corpus (5)

• Analytic treatment of IR-spectroscopy data for double well potential
• Calculation of IR absorption intensities for hydrogen bond from exactly solvable Schrödinger equation
• Exactly solvable double-well potential in Schrödinger equation for inversion mode of phosphine molecule
• Model for vibrationally enhanced tunneling of proton transfer in hydrogen bond
• Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart