A simple interpolation formula for the spectra of power-law and log potentials

Details A simple interpolation formula for the spectra of power-law and log potentials A simple interpolation formula for the spectra of power-law and log potentials

2000-04-11

arxiv.org/abs/math-ph/0004010v1

J. Phys. G 26, 981-986 (2000)

Physics

Mathematical Physics

7 pages, 2 figures

Scientific paper

10.1088/0954-3899/26/6/401

Non-relativistic potential models are considered of the pure power V(r)=sgn(q) r^q and logarithmic V(r)=ln(r) types. It is shown that, from the spectral viewpoint, these potentials are actually in a single family. The log spectra can be obtained from the power spectra by the limit q --> 0 taken in a smooth representation P(n,l,q) for the eigenvalues E(n,l,q). A simple approximation formula is developed which yields the first thirty eigenvalues with error < 0.04%.

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