The S-matrix for abstract scattering systems

✍ Scribed by W. O. Amrein; D. B. Pearson

• Publisher: Springer
• Year: 1979
• Tongue: English
• Weight: 154 KB
• Volume: 3
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00400060

✦ Synopsis

scattering system. We derive a bound, in terms of the interaction, on integrals of the form f h(X)IIS(X) --l II~s dX, where [I-liras denotes the Hilbert-Schmidt norm.

There are various abstract methods in scattering theory for proving that the S-matrix S(X) is such that, at almost all energies X, R(X) -= S(X) -I is a trace class operator [1][2][3]. Since in quantum mechanics the total scattering cross-section is proportional to the square of the Hilbert-Schmidt Letters in Mathematical Physics 3 (1979) 83 -86.