Variational Analysis for a Generalized Spiked Harmonic Oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator − d dx2 +Bx+ A x2 + λ x , where α is a real positive parameter. The formalism makes use of a basis provided by exact solutions of Schrödinger’s equation for the Gol’dman and Krivchenkov Hamiltonian, and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension D 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.