# Asymptotic expansions of Mathieu functions in wave mechanics

## Abstract

Solutions of the radial Schroedinger equation containing a polarization potential r/sup -4/ are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states.

- Authors:

- Publication Date:

- OSTI Identifier:
- 7106275

- Resource Type:
- Journal Article

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

- Additional Journal Information:
- Journal Volume: 21:3

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; SCHROEDINGER EQUATION; ASYMPTOTIC SOLUTIONS; BOUND STATE; FUNCTIONS; ION-ATOM COLLISIONS; ION-MOLECULE COLLISIONS; MATHIEU EQUATION; NUMERICAL SOLUTION; PHASE SHIFT; POLARIZATION; SCATTERING; SERIES EXPANSION; ATOM COLLISIONS; COLLISIONS; DIFFERENTIAL EQUATIONS; EQUATIONS; ION COLLISIONS; MOLECULE COLLISIONS; WAVE EQUATIONS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; 640304 - Atomic, Molecular & Chemical Physics- Collision Phenomena

### Citation Formats

```
Hunter, G, and Kuriyan, M.
```*Asymptotic expansions of Mathieu functions in wave mechanics*. United States: N. p., 1976.
Web. doi:10.1016/0021-9991(76)90028-0.

```
Hunter, G, & Kuriyan, M.
```*Asymptotic expansions of Mathieu functions in wave mechanics*. United States. https://doi.org/10.1016/0021-9991(76)90028-0

```
Hunter, G, and Kuriyan, M. Thu .
"Asymptotic expansions of Mathieu functions in wave mechanics". United States. https://doi.org/10.1016/0021-9991(76)90028-0.
```

```
@article{osti_7106275,
```

title = {Asymptotic expansions of Mathieu functions in wave mechanics},

author = {Hunter, G and Kuriyan, M},

abstractNote = {Solutions of the radial Schroedinger equation containing a polarization potential r/sup -4/ are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states.},

doi = {10.1016/0021-9991(76)90028-0},

url = {https://www.osti.gov/biblio/7106275},
journal = {J. Comput. Phys.; (United States)},

number = ,

volume = 21:3,

place = {United States},

year = {1976},

month = {7}

}

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