# Series solutions and the variational principle

## Abstract

The B matrix method of Frost for solution of nonseparable Schroedinger equations is used in combination with the upper bound theorem for linear variation functions to show that series solutions are possible in the general case without explicit evaluation of integrals. The procedures are illustrated with calculations on the hydrogen-molecule ion, with some discussion of the helium atom.

- Authors:

- Publication Date:

- Research Org.:
- Department of Chemistry, Saint John's University, Collegeville, Minnesota 56321

- OSTI Identifier:
- 6197226

- Resource Type:
- Journal Article

- Journal Name:
- J. Chem. Phys.; (United States)

- Additional Journal Information:
- Journal Volume: 70:3

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ELECTRONIC STRUCTURE; VARIATIONAL METHODS; HELIUM; HYDROGEN IONS; MOLECULAR IONS; SCHROEDINGER EQUATION; CHARGED PARTICLES; CRYOGENIC FLUIDS; DIFFERENTIAL EQUATIONS; ELEMENTS; EQUATIONS; FLUIDS; IONS; NONMETALS; RARE GASES; WAVE EQUATIONS; 640305* - Atomic, Molecular & Chemical Physics- Atomic & Molecular Theory- (-1987)

### Citation Formats

```
Rioux, F., and Harriss, D.K.
```*Series solutions and the variational principle*. United States: N. p., 1979.
Web. doi:10.1063/1.437594.

```
Rioux, F., & Harriss, D.K.
```*Series solutions and the variational principle*. United States. doi:10.1063/1.437594.

```
Rioux, F., and Harriss, D.K. Thu .
"Series solutions and the variational principle". United States. doi:10.1063/1.437594.
```

```
@article{osti_6197226,
```

title = {Series solutions and the variational principle},

author = {Rioux, F. and Harriss, D.K.},

abstractNote = {The B matrix method of Frost for solution of nonseparable Schroedinger equations is used in combination with the upper bound theorem for linear variation functions to show that series solutions are possible in the general case without explicit evaluation of integrals. The procedures are illustrated with calculations on the hydrogen-molecule ion, with some discussion of the helium atom.},

doi = {10.1063/1.437594},

journal = {J. Chem. Phys.; (United States)},

number = ,

volume = 70:3,

place = {United States},

year = {1979},

month = {2}

}

DOI: 10.1063/1.437594

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