An alternative series solution to the isotropic quartic oscillator inN dimensions

Part of theD-dimensional spiked harmonic oscillator spectra

“…for odd D. For more details the reader may refer to ref.s [17,18,27]. We therefore calculate, in section 3, the energies for D = 2 and D = 3 spiked harmonic oscillators, for a given number of nodes k and different values of l, and construct part of its D -dimensional bound -state spectra.…”

Exploiting the interdependence of maximum entropy parameters in eigenvalue problems

“…Thus, we improve considerably the prevalent formalism 9–14. We modify the MEP ansatz 13, 14 to ensure the correct small‐ and large‐ x behavior of the generated wave function. These latter characteristics are readily derived 15–17 even if the problem at hand is not analytically tractable. Here, optimization is performed without resorting to the energy minimum principle or the MEP; instead, the moment recursion relations are profitably utilized. We do not require the explicit values of any of the moments at any stage. It is sufficient to assume that the moments exist, and are finite. Our scheme is general; it applies to potentials expressible as rational functions. The method is numerically stable, yielding highly accurate results at the expense of little computational labor.…”

“…We modify the MEP ansatz 13, 14 to ensure the correct small‐ and large‐ x behavior of the generated wave function. These latter characteristics are readily derived 15–17 even if the problem at hand is not analytically tractable.…”