Algebraic approach to the spectral problem for the Schrodinger equation with power potentials

The method reducing the solution of the Schrodinger equation for several ty pes of power potentials to the solution of the eigenvalue problem for the i nfinite system of algebraic equations is developed. The finite truncation o f this system provides high accuracy results for low-lying levels. The prop osed approach is appropriate both for analytic calculations and for numeric al computations. This method allows also to determine the spectrum of the S chrodinger-like relativistic equations. The heavy quarkonium (charmonium an d bottomonium) mass spectra for the Cornell potential and the sum of the Co ulomb and oscillator potentials are calculated. The results are in good agr eement with experimental data.