Algebraic Approach to the Spectral Problem for the Schrödinger Equation With Power Potentials

Abstract

The method reducing the solution of the Schrödinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system provides high accuracy results for low-lying levels. The proposed approach is appropriate both for analytic calculations and for numerical computations. This method allows also to determine the spectrum of the Schrödinger-like relativistic equations. The heavy quarkonium (charmonium and bottomonium) mass spectra for the Cornell potential and the sum of the Coulomb and oscillator potentials are calculated. The results are in good agreement with experimental data.

Bound Energy Masses of Mesons Containing the Fourth Generation and Iso-Singlet Quarks

“…Firstly, we calculate the masses of bound states of cc and bb in Table 1 for the two potential types. It is seen that our results are in good agreement with the experimental results [23,24]. In Table 2, we present the masses of bound states of quarkonia and mesons formed by the fourth SM family up-type quark and E 6 isosinglet quark, respectively.…”

New Hadrons Formed by the Fourth Sm Family and Iso-Singlet Quarks

“…With these parameters, we calculate the masses of bound states of cc and bb, which are given in Table 1. It is seen that our results are in good agreement with experimental data [11] (for comparison see [12,13]).…”

R-matrix calculations for few-quark bound states

“…The parameters of potentials are a = 0.18 GeV 2 , b = −0.29 GeV with α s = 0.47 for charmonium (m c = 1.56 GeV) and α s = 0.39 for bottomonium (m b = 4.93 GeV). As we have shown in Table 1, our numerical results for masses of charmonium and bottomonium, obtained by R-matrix method are in excellent agreement with solution of Lippmann-Schwinger integral equation in momentum [7] and configuration [22] spaces and also with the experimental data [23].…”

“…We have used the linear confining plus Coulomb potential of Eq. (18) Table 1, our numerical results for masses of charmonium and bottomonium, obtained by the R-matrix method, are in excellent agreement with the solution of the Lippmann-Schwinger integral equation in momentum space [7] and configuration space [23], and also with the experimental data [24].…”