  A variational analysis is presented for the generalized spiked harmonic
oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 +
lambda/x^alpha, and alpha and lambda are real positive parameters. The
formalism makes use of a basis provided by exact solutions of Schroedinger's
equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the
corresponding matrix elements that were previously found. For all the discrete
eigenvalues the method provides bounds which improve as the dimension of the
basis set is increased. Extension to the N-dimensional case in arbitrary
angular-momentum subspaces is also presented. By minimizing over the free
parameter A, we are able to reduce substantially the number of basis functions
needed for a given accuracy.
