  The method reducing the solution of the Schroedinger 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
Schroedinger-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.
