Study of Wave Equations Involving Iterated Laplacian and Potential <math>;r-β </math> by the <math>1/N</math> Method

Physics NotePublished

Study of Wave Equations Involving Iterated Laplacian and Potential $<math>\;r^{-\beta }</math>$ by the $<math>1/N</math>$ Method

C.G. Bollini; J. J. Giambiagi; J. S. Helman

1990

Authors: C.G. Bollini; J. J. Giambiagi; J. S. Helman
Type: Physics Note
Status: Published
Publication date: 1990
Description: The relation between the potential <math>r^{-\beta}\,\!</math> and the asymptotic behavior of the eigenvalues of the ordinary wave equation for space dimension <math> N \rightarrow \infty\,\!</math> is found. An analogous relation is discussed when the wave equation involves an iterated Laplacian. A criterion is given to determine when a potential should be considered singular, depending on the space dimension and the degree of iteration of the Laplacian. Finally, a modification is suggested for the approximation proposed by Witten which sensibly improves the results for the ground state energy of the hydrogen and helium atoms.
Year: 1990
Number: CBPF-NF-017/90
Linked to a thesis: No
Linked to a grant: No