### Abstract

A simple plane wave solution of the Schrodinger-Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J. Leech et al., Phys. Rev. Lett. 88. 257901 (2002)). The problem is resolved via non- uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.

Original language | English |
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Pages (from-to) | 17-20 |

Number of pages | 4 |

Journal | Physica Scripta |

Volume | 70 |

Issue number | 1 |

Publication status | Published - Jul 2004 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

Mulligan, P. G., & Crothers, D. (2004). Plane wave and Coulomb asymptotics.

*Physica Scripta*,*70*(1), 17-20.