ENERGY HOUNDS FOR THE SPIKED HARMONIC-OSCILLATOR

A three-parameter variational trial function is used to determine an u pper bound to the ground-state energy of the spiked harmonic-oscillato r Hamiltonian H = -d(2)/dx(2) + x(2) + lambda/\X\(alpha). The entire p arameter range lambda > 0 and alpha greater than or equal to 1 is trea ted in a single elementary formulation. The method of potential envelo pes is also employed to derive a complementary energy lower bound form ula valid for all the discrete eigenvalues.