𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Accurate non-perturbative solution of eigenvalue problems with application to anharmonic oscillator

✍ Scribed by K. Banerjee

Publisher
Springer
Year
1976
Tongue
English
Weight
242 KB
Volume
1
Category
Article
ISSN
0377-9017

No coin nor oath required. For personal study only.

✦ Synopsis

A method for eigenvalue problems is presented. As an example, we have obtained very accurate eigenvalues and eigenfunctions of the quartic artharmonic oscillator.

The method is non-perturbative and involves the use of an appropriately scaled set of basis functions for the determination of each eigenvalue. The claimed accuracy for all eigenvalues is 15 significant figures. The method does not deteriorate for higher eigenvalues.

πŸ“œ SIMILAR VOLUMES

Perturbation of null spaces with applica
Perturbation of null spaces with application to the eigenvalue problem and generalized inverses
✍ Konstantin E. Avrachenkov; Moshe Haviv πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 208 KB

We consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors

Solution of the matrix eigenvalue proble
Solution of the matrix eigenvalue problem with applications to the study of free linear dynamical systems
✍ L. Kohaupt πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 330 KB

The new idea is to study the stability behavior of the solution x = x(t) of the initial value problem αΊ‹ = Ax, t t 0 , x(t 0 ) = x 0 , with A ∈ C nΓ—n , in a weighted (semi-) norm β€’ R where R is taken as an appropriate solution of the matrix eigenvalue problem RA + A \* R = R, rather than as the solut