Analytic solution of the Schrödinger equation for the Coulomb-plus-linear potential. I. The wave functions

We solve the Schrodinger equation for a quark–antiquark system interacting via a Coulomb-plus-linear potential, and obtain the wave functions as power series, with their coefficients given in terms of the combinatorics functions.

[1]  Kenneth H. Rosen,et al.  Discrete Mathematics and its applications , 2000 .

[2]  E. Eichten,et al.  The Spectrum of Charmonium , 1974 .

[3]  A. F. Antippa,et al.  Topological solution for systems of simultaneous linear equations , 1979 .

[4]  John D. Stack Heavy quark potential in SU(2) lattice gauge theory , 1983 .

[5]  E. Eichten,et al.  Charmonium: The Model , 1978 .

[6]  B. Thidé,et al.  Phase-integral treatment of the linear plus Coulomb potential. I. Energy levels , 1985 .

[7]  C. H. Mehta,et al.  Nonperturbative approach to screened Coulomb potentials , 1978 .

[8]  C. Quigg,et al.  Quantum Mechanics with Applications to Quarkonium , 1979 .

[9]  A. F. Antippa Discrete path approach to linear recursion relations , 1977 .

[10]  M Znojil,et al.  The Hill determinant approach to the Coulomb plus linear confinement , 1987 .

[11]  Exact Closed Form Solution for Two Coupled Inhomogeneous First Order Difference Equations with Variable Coefficients , 2002 .

[12]  B. Jeffreys,et al.  Functions of Mathematical Physics , 1970 .

[13]  S. Vasan,et al.  Analytic WKB energy expression for the linear plus Coulomb potential , 1983 .

[14]  E. Austin Perturbation theory and Padé approximants for a hydrogen atom in an electric field , 1980 .

[15]  Bohr-Sommerfeld quantization and meson spectroscopy , 2000, hep-ph/0412170.

[16]  Chen,et al.  Energies of quark-antiquark systems, the Cornell potential, and the spinless Salpeter equation. , 1993, Physical review. D, Particles and fields.

[17]  Chhajlany Sc,et al.  Study of the potential V=-a/r+br. , 1991 .

[18]  Complete O(v 2 ) corrections to the static interquark potential from SU(3) gauge theory , 1997, hep-lat/9703019.

[19]  R. Saxena,et al.  Polynomial perturbation of a hydrogen atom , 1982 .

[20]  J. Killingbeck Perturbation theory without wavefunctions , 1978 .

[21]  A. J. Phares,et al.  The linear potential: A solution in terms of combinatorics functions , 1978 .

[22]  General formalism solving linear recursion relations , 1977 .

[23]  I. Dremin,et al.  Potential models of quarkonium , 1984 .

[24]  M. Chaichian,et al.  Coupling constants and the nonrelativistic quark model with charmonium potential , 1980 .