METHOD FOR CALCULATING ANALYTICAL SOLUTIONS OF THE SCHRODINGER-EQUATION - ANHARMONIC-OSCILLATORS AND GENERALIZED MORSE OSCILLATORS

A method for calculating the analytical solutions of the one-dimension al Schrodinger equation is suggested. A general discussion of the poss ible forms of the potentials and wave functions that are necessary to get the analytical solution is presented. In general, the analytical s olutions appear in multiplets corresponding to the quantum number n of the harmonic oscillator As an application, known solutions for the an harmonic oscillators are critically recalculated and a few additional results are found. Analytical solutions are also found for the general ized Morse oscillators.