Existence of the Møller wave operators for V(r)=γ sin(μrα)rβ

✍ Scribed by John D Dollard; Charles N Friedman

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 618 KB
• Volume: 111
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(78)90230-0

✦ Synopsis

We prove the existence of the Msller wave operators and the unitarity of the S operator for quantum mechanical potential scattering by potentials of the form &PER X sin(pP) 0 < 01)

This includes the Special case V(r) = sin(r)/r.

In the present article we shall consider nonrelativistic quantum mechanical scattering in 3 space dimensions by radial potentials of the form (0.1)

We shail prove the existence of the Msller wave operators L?* and the unitarity of the S operator, S = (Q+)* Sz-. Our method is applicable to potentials other than those cited, but these are representative of the scope of applicability of the method. A primary step in our argument is a careful analysis of the asymptotic behavior of solutions of the radial SchrGdinger equation (0.2) -I(1 + 1) fg+T + V(r) 9 = ET, E > 0, for potentiak of the form (0.1); the results are apparently new and arose from the authors' study of product integration methods [6-91. The rest of the argument was 251