Analytic solutions to the problem of Coulomb and confining potentials

The oscillator-representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain analytic results for arbitrary values of the parameters specifying the above-type potentials. The calculated energies of the ground and excite d states of the quantum systems in question are found to comply well with e xact results.