A time-dependent, two Hilbert space approach to long-range quantum scattering
✍ Scribed by Denis A. W. White
- Publisher
- Springer
- Year
- 1986
- Tongue
- English
- Weight
- 260 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0377-9017
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✦ Synopsis
Scattering of a quantum mechanical particle by a long-range potential is studied using Enss's time-dependent method. More precisely, a simple and natural extension of the Enss method to a two Hilbert space setting is established. Applied to the consideration of long-range scattering, this extended Enss method reduces the problem of proving existence and completeness of the wave operators to the problem of solving an eikonal equation on a cone in phase space. Relying on a solution of the eikonal equation constructed by Isozaki and Kitada, it is shown that the wave operators exist and are complete whenever the potential is in the long-range class introduced by H6rmander.