Bessel basis with applications: N-dimensional isotropic polynomial oscillators

The efficient technique of expanding the wave function into a Fourier-Bessel series to solve the radial Schrodinger equation with polynomial potentials, V(r) = Sigma(i=1)(K) v(2i)r(2i), in two dimensions is extended to N-dimensional space. It is shown that the spectra of two- and three-dimensional oscillators cover the spectra of the corresponding N-dimensional problems for all N. Extremely accurate numerical results are presented for illustrative purposes. The connection between the eigenvalues of the general anharmonic oscillators and the confinement potentials of the farm V(r) = -Z/r + Sigma(i=1)(K-1) c(i)r(i) is also discussed. (C) 1997 John Wiley & Sons, Inc