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A perturbed generalized eigenvalue equation for the helium atom

✍ Scribed by C. Laughlin; A. T. Amos

Publisher
John Wiley and Sons
Year
1970
Tongue
English
Weight
427 KB
Volume
4
Category
Article
ISSN
0020-7608

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✦ Synopsis

Abstract

The Schrödinger equation for helium is written as a generalized eigenvalue equation and this is solved perturbatively for the ground state. The zero order equation is taken to be that of a “six‐dimensional hydrogen atom” since, in generalized eigenvalue form, this has a discrete spectrum. Although the zero‐order wave function is very poor and gives only 86% of the energy the perturbation procedure is able to improve this to 99% through third‐order.

📜 SIMILAR VOLUMES

A perturbed generalized eigenvalue equat
A perturbed generalized eigenvalue equation for the hydrogen molecular ion
✍ M. R. Woodward 📂 Article 📅 1972 🏛 John Wiley and Sons 🌐 English ⚖ 279 KB

## Abstract The Schrödinger equation for the hydrogen molecular ion is written as a perturbed united atom which is then treated as a generalized eigenvalue equation. The ground state energy is calculated through third order for small internuclear distances.

Brillouin-Wigner perturbation theory and
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✍ C. Laughlin; M. R. Woodward; A. T. Amos 📂 Article 📅 1974 🏛 John Wiley and Sons 🌐 English ⚖ 340 KB

## Abstract A Brillouin‐Wigner perturbation expansion is derived for the generalized eigenvalue equation (__F__~0~ + __F__~1~)Ψ = μ__A__Ψ. The theory is applied through second order to calculate the ground‐state energies of the helium atom and the hydrogen molecular ion. The results are compared wi

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A frequently encountered scenario in structural dynamics is determining the changes in the eigensolution of a system after certain modi"cations are introduced. Clearly, if these modi"cations are substantial, then a new analysis and computational cycle are necessary in order to compute the new eigend