ISSN:
0018-019X
Keywords:
Chemistry
;
Organic Chemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
A method for calculating the eigenvalues of a particle moving in a one-dimensional potential, given as V(ξ) = υ1 ξ + υ2ξ2 + υ3ξ3 +… is described. It is a variational method which makes use of linear combinations of HERMITE orthogonal functions \documentclass{article}\pagestyle{empty}\begin{document}$ \Phi (\xi) = \sum\limits_{n = 0}^{N - 1} {c_n u_n } (\xi) $\end{document}, the recursion properties of which allow for the calculation of the matrix elements Hnm and Snm in closed form without involving any further approximation. As the matrix H = (Hnm) is a band matrix, the corresponding eigenvalue problem can be solved by applying the LR-transformation, which yields the eigenvalues in the order of their stability, so that the calculation may be stopped after the required number of the lowest levels has been calculated.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/hlca.19590420702
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