Variational spiked oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian –d²/dr² +r² +/r^5/2,>0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).