# Crater property in two-particle bound states: When and why

## Abstract

Crater has shown that, for two particles (with masses m{sub 1} and m{sub 2}) in a Coulombic bound state, the charge distribution is equal to the sum of the two charge distributions obtained by taking m{sub 1}{yields}{infinity} and m{sub 2}{yields}{infinity}, respectively, while keeping the same Coulombic potential. We provide a simple scaling criterion to determine whether an arbitrary Hamiltonian possesses this property. In particular, we show that, for a Coulombic system, fine structure corrections preserve this Crater property while two-particle relativistic corrections and/or hyperfine corrections may destroy it. (c) 2000 American Association of Physics Teachers.

- Authors:

- Department of Physics, University of Maryland, College Park, Maryland 20742-4111 (United States)

- Publication Date:

- OSTI Identifier:
- 20216355

- Resource Type:
- Journal Article

- Journal Name:
- American Journal of Physics

- Additional Journal Information:
- Journal Volume: 68; Journal Issue: 6; Other Information: PBD: Jun 2000; Journal ID: ISSN 0002-9505

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; SCHROEDINGER EQUATION; COULOMB CORRECTION; COULOMB ENERGY; COULOMB FIELD; BOUND STATE; HAMILTONIANS; PERTURBATION THEORY; RELATIVISTIC RANGE; HYPERFINE STRUCTURE; ELECTRONIC STRUCTURE; EDUCATIONAL TOOLS; QUANTUM MECHANICS; THEORETICAL DATA

### Citation Formats

```
Chow, Chi-Keung.
```*Crater property in two-particle bound states: When and why*. United States: N. p., 2000.
Web. doi:10.1119/1.19482.

```
Chow, Chi-Keung.
```*Crater property in two-particle bound states: When and why*. United States. doi:10.1119/1.19482.

```
Chow, Chi-Keung. Thu .
"Crater property in two-particle bound states: When and why". United States. doi:10.1119/1.19482.
```

```
@article{osti_20216355,
```

title = {Crater property in two-particle bound states: When and why},

author = {Chow, Chi-Keung},

abstractNote = {Crater has shown that, for two particles (with masses m{sub 1} and m{sub 2}) in a Coulombic bound state, the charge distribution is equal to the sum of the two charge distributions obtained by taking m{sub 1}{yields}{infinity} and m{sub 2}{yields}{infinity}, respectively, while keeping the same Coulombic potential. We provide a simple scaling criterion to determine whether an arbitrary Hamiltonian possesses this property. In particular, we show that, for a Coulombic system, fine structure corrections preserve this Crater property while two-particle relativistic corrections and/or hyperfine corrections may destroy it. (c) 2000 American Association of Physics Teachers.},

doi = {10.1119/1.19482},

journal = {American Journal of Physics},

issn = {0002-9505},

number = 6,

volume = 68,

place = {United States},

year = {2000},

month = {6}

}

DOI: 10.1119/1.19482

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.