The study of exactly solvable problems has attracted much attention of many authors since the early development of quantum mechanics. To our knowledge, the exact solvable physical problems are few in quantum mechanics except for several well-known exactly solvable quantum systems like the hydrogen atom, harmonic oscillator and others. Due to its mathematical advantages, the harmonic oscillator model has been widely used to describe the interaction force of the diatomic molecule. Nevertheless, it is well known that the real molecular vibrations are anharmonic. Among many molecular potentials, the Morse potential as an ideal and typical anharmonic potential permits an exactly mathematical treatment and it has been the subject of interest since it was proposed by Morse in 1929 . In particular, the Morse potential will reduce to the harmonic oscillator in the harmonic limit.
KeywordsMatrix Element Harmonic Oscillator Diatomic Molecule Factorization Method Dynamic Group
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