Geodesic
Spectral problem for the radial Schr\''odinger equation with power confining potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 3, pp. 397-412

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An approach reducing the solution of the Schrödinger equation for some widely used power potentials to the solution of the eigenvalue problem for an infinite system of algebraic equations is proposed. The developed algorithm is appropriate both for analytic calculations and for numerical computations. On the basis of this method, the charmonium and bottomonium mass spectra are calculated for the Cornell potential and for the sum of the Coulomb and oscillator potentials. The proposed approach allows one to determine the mass spectrum of the relativistic Schrödinger-like equations. Good agreement with experimental data is achieved. 
@article{TMF_1997_113_3_a3,
     author = {A. S. Vshivtsev and V. O. Galkin and A. V. Tatarintsev and R. N. Faustov},
     title = {Spectral problem for the radial {Schr\''odinger} equation with power confining potentials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {397--412},
     publisher = {mathdoc},
     volume = {113},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_3_a3/}
}
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A. S. Vshivtsev; V. O. Galkin; A. V. Tatarintsev; R. N. Faustov. Spectral problem for the radial Schr\''odinger equation with power confining potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 3, pp. 397-412. http://geodesic.mathdoc.fr/item/TMF_1997_113_3_a3/