Bohr Sommerfeld quantisation and molecular potentials

Abstract

We combine, within the Bohr Sommerfeld quantization rule, a systematic perturbation with asymptotic analysis of the action integral for potentials which support a finite number of bound states with E < 0 to obtain an interpolation formula for the energy eigenvalues. We find interpolation formulae for the Morse potential as well as potentials of the form V = V 0 a x 2k − a x k . For k = 6 i.e. the well known Lennard Jones potential this yields results within 1 per cent of the highly accurate numerical values. For the Morse potential this procedure yields the exact answer. We find that the result for the Morse potential which approaches zero exponentially is the k → ∞ limit of the Lennard Jones class of potentials.

WKB approximation under Killingbeck potential and its application to double heavy meson mass spectrum

“…Moreover, the authors in Refs. [15][16][17][18][19][20][21][22] have used WKB method to study mass spectra under various potential energies. The bound state solution to the wave equations under the quark-antiquark interaction potential functions such as the Killingbeck or the Cornell potential have attracted much research interest in high energy physics [18].…”