# Local properties of three-body atomic wave functions

## Abstract

The local properties and accuracy of the positronium negative-ion (Ps{sup -}) ground-state wave functions obtained by the stochastic variational method (SVM) and by direct solution of the Schroedinger equation with the help of the correlation-function hyperspherical-harmonic method (CFHHM) are studied and compared. Though the energy, calculated by both methods, agrees to up to ten digits, the amplitudes of the values of the operator D=H{psi}/E{psi}-1, characterizing local deviation of the wave function from its true value, in all of the coordinate space in the SVM are consistently larger (by up to five orders of magnitude) than in the CFHHM, despite the fact that the SVM observables except <{delta}(r{sub k})> converge to significantly more digits than the CFHHM observables for their respective selected bases. (c) 2000 The American Physical Society.

- Authors:

- Department of Theoretical Physics, J. Stefan Institute, P.O. Box 3000, 1001 Ljubljana, (Slovenia)
- Racah Institute of Physics, Hebrew University, Jerusalem 91904, (Israel)
- Physics Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439 (United States)

- Publication Date:

- OSTI Identifier:
- 20216553

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 6; Other Information: PBD: Jun 2000; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; POSITRONIUM; WAVE FUNCTIONS; GROUND STATES; CORRELATION FUNCTIONS; ACCURACY; HARMONICS; VARIATIONAL METHODS; QUANTUM OPERATORS; THEORETICAL DATA

### Citation Formats

```
Krivec, R., Mandelzweig, V. B., and Varga, K.
```*Local properties of three-body atomic wave functions*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevA.61.062503.

```
Krivec, R., Mandelzweig, V. B., & Varga, K.
```*Local properties of three-body atomic wave functions*. United States. doi:10.1103/PhysRevA.61.062503.

```
Krivec, R., Mandelzweig, V. B., and Varga, K. Thu .
"Local properties of three-body atomic wave functions". United States. doi:10.1103/PhysRevA.61.062503.
```

```
@article{osti_20216553,
```

title = {Local properties of three-body atomic wave functions},

author = {Krivec, R. and Mandelzweig, V. B. and Varga, K.},

abstractNote = {The local properties and accuracy of the positronium negative-ion (Ps{sup -}) ground-state wave functions obtained by the stochastic variational method (SVM) and by direct solution of the Schroedinger equation with the help of the correlation-function hyperspherical-harmonic method (CFHHM) are studied and compared. Though the energy, calculated by both methods, agrees to up to ten digits, the amplitudes of the values of the operator D=H{psi}/E{psi}-1, characterizing local deviation of the wave function from its true value, in all of the coordinate space in the SVM are consistently larger (by up to five orders of magnitude) than in the CFHHM, despite the fact that the SVM observables except <{delta}(r{sub k})> converge to significantly more digits than the CFHHM observables for their respective selected bases. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevA.61.062503},

journal = {Physical Review. A},

issn = {1050-2947},

number = 6,

volume = 61,

place = {United States},

year = {2000},

month = {6}

}