Application of an improved variational method to the D-dimensional generalized anharmonic oscillator

A recently improved systematic variational scheme is applied to the determination of the energy of the ground state and first even-parity excited state of a single-well anharmonic oscillator and of a bidimensional anharmonic isotropic oscillator, If we use the deepest local minimum in the energy in function of a single variational parameter we obtain closer results to the exact values for small N truncation, We use another variational parameter which illustrate better the increase of the nonperturbed Hamiltonian and decrease of the perturbation. (C) 2002 Elsevier Science B.V. All rights reserved.