Место издания:Universite de Bourgogne Dijon, France
Первая страница:403
Последняя страница:403
Аннотация:The common problem with existing methods for solving the many-body vibrational Schr ̈odinger equation is insufficient flexibility of the zero-order approximation, often chosen in the form of a harmonic oscillator. The Morse oscillator is much closer to actual one-dimensional intramolecular potentials. An essential element of modern theoretical approaches in this field is the fundamental technique of ladder (creation/annihilation) operators. Finding suitable ladder operators for solvable anharmonic oscillators and mainly the Morse oscillator remain one of the major challenges of nuclear vibrational dynamics. Employing Morse oscillator ladder operators can open new horizons in accurate calculations of vibrational properties and/or simplify solutions of problems based on the Morse potential as the zero-order approximation.
We provide a detailed consideration of various approaches to constructing ladder operators for the Morse oscillator, study their properties, analyze problems and propose some variants of applying existing forms of ladder operators to certain methods of solving the anharmonic vibrational problem [1].
The quasi-number states (QNS) wave functions introduced earlier have mathematical structure very close to native functions of the Morse oscillator [2]. In the QNS basis the Morse has a tridiagonal matrix representation, factorized into a finite bound states part and an infinite part for scattering states. The ladder operators that connect QNS states are appropriate ones for the analysis of a perturbed Morse oscillator and for constructing a scheme for solving the perturbed many-dimensional problem.
The QNS-based approach is suitable for all matrix element-based approaches: the vibrational configuration interaction (VCI) variational method, the VSCF method and its extensions (VSCF/MPn, VSCF/VCI, etc), the vibrational coupled cluster (VCC) method and possibly the matrix form of the Van Vleck perturbation theory.
[1] doi:10.1080/0144235X.2019.1593583, S. V. Krasnoshchekov and X. Chang, Int. Rev. Phys. Chem., 38, 63–113 (2019).
[2] doi:10.1088/0305-4470/37/5/023, R. Lemus, J.M. Arias and J. Go ́mez-Camacho, J. Phys. A: Math. Gen., 37, 1805–1820 (2004).
