Perturbational and variational treatments of the Morse oscillator |
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| Affiliation: | 1. Mechanical and Aerospace Engineering, Center for Advanced Turbomachinery and Energy Research, University of Central Florida, Orlando, FL 32816, USA;2. Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;1. Sichuan University, Chengdu 610064, Sichuan, China;2. Xi''an Modern Chemistry Research Institute, Xi''an 710065, Shaanxi, China;1. Cluster of Applied Sciences, Open University Malaysia, Malaysia;2. Research Center for Quantum Physics, Huzhou University, Huzhou 313000, China;3. Laboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, UPALM, C.P. 07700, CDMX, Mexico |
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| Abstract: | The Morse oscillator hamiltonian is expressed as an infinite expansion in powers of a natural perturbation parameter, the square root of the anharmonicity constant, relative to the simple harmonic oscillator as zeroth-order hamiltonian. A transformation of variables leads to a hamiltonian which involves terms no higher than second order in this natural perturbation parameter. In both cases, the exact bound state eigenvalues of the Morse oscillator are given by second-order perturbation theory. The Schrödinger equation corresponding to the transformed Morse hamiltonian is solved variationally, via a complete set expansion in simple harmonic oscillator eigenstates. Accurate approximations to the exact eigenvalues and eigenfunctions of bound states of the Morse oscillator can be obtained for all but the very highest levels. |
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