A simple interpolation formula for the spectra of power-law and log potentials
Richard L Hall; Richard L Hall; Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, Québec, Canada H3G 1M8
Журнал:
Journal of Physics G: Nuclear and Particle Physics
Дата:
2000-06-01
Аннотация:
Non-relativistic potential models are considered of the pure power V(r) = sgn(q) r <sup>q</sup> 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<sub>nℓ</sub>(q) for the eigenvalues E<sub>nℓ</sub>(q). A simple approximation formula is developed which yields the first 30 eigenvalues with an error less than 0.04%.
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