Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator

摘要

The power series method has been adapted to compute the spectrum of theSchrodinger equation for central potential of the form $V(r)={d_{-2}\overr^2}+{d_{-1}\over r}+\sum_{i=0}^{\infty} d_{i}r^i$. The bound-state energiesare given as zeros of a calculable function, if the potential is confined in aspherical box. For an unconfined potential the interval bounding the energyeigenvalues can be determined in a similar way with an arbitrarily chosenprecision. The very accurate results for various spherically symmetricanharmonic potentials are presented.