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Exact solutions for vibrational levels of the Morse potential

The vibrational levels of diatomic molecules via Morse potentials are studied by means of the system confined in a spherical box of radius l, II is shown that there exists a critical radius l(cr),, at which the spectrum of the usual unbounded system can be calculated to any desired accuracy. The results are compared with those of Morse's classical solution which is based on the assumption that the domain of the internuclear distance r includes the unphysical region (-infinity, 0). By determining numerically exact lower and upper bounds for the energy eigenvalues of Li-2 molecule, it is deduced here that Morse's approach is perfect and gives very impressive results.