A simple interpolation formula for the spectra of power-law and log potentials
Hall, Richard L.
arXiv, 0004010 / Harvested from arXiv
Text on arXiv
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%.
Publié le : 2000-04-10
Classification:  Mathematical Physics,  High Energy Physics - Phenomenology 
@article{0004010,
     author = {Hall, Richard L.},
     title = {A simple interpolation formula for the spectra of power-law and log
  potentials},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0004010}
}

Hall, Richard L. A simple interpolation formula for the spectra of power-law and log
  potentials. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0004010/