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 $N{H}_3$.

arXiv comment16 pages, 2 figures, Final version, misprint in Appendix 1 has been corrected

References in corpus (18)

• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• Tunnel splittings for one dimensional potential wells revisited
• On a solution of the Schrodinger equation with a hyperbolic double-well potential
• Perspective: Tipping the scales - search for drifting constants from molecular spectra
• Magnetic quantum dots and rings in two dimensions
• Tunneling and energy splitting in an asymmetric double-well potential
• Bound states in a hyperbolic asymmetric double-well
• Semi-classical formula for quantum tunneling in asymmetric double-well potentials
• Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)
• Exactly solvable Schrödinger equation with double-well potential for hydrogen bond
• Two-electron atom with a screened interaction
• Solving systems of transcendental equations involving the Heun functions
• Localization or tunneling in asymmetric double-well potentials
• New relations for the derivative of the confluent Heun function
• Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model
• Exact solution of Smoluchowski's equation for reorientational motion in Maier-Saupe potential
• Probability distribution function for reorientations in Maier-Saupe potential

Cited by in corpus (8)

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• Analytic treatment of IR-spectroscopy data for double well potential
• Model for vibrationally enhanced tunneling of proton transfer in hydrogen bond
• Exactly solvable double-well potential in Schrödinger equation for inversion mode of phosphine molecule
• Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart
• Schrödinger equation with Pauli-Fierz Hamiltonian and double well potential as model of vibrationally enhanced tunneling for proton transfer in hydrogen bond
• Non-standard quantum algebras and infinite-dimensional PT-symmetric systems