Vol. 31, No. 1, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
The asymptotic behavior of the Klein-Gordon equation with external potential. II

John Martin Chadam

Vol. 31 (1969), No. 1, 19–31
Abstract

Let U0(t) and U(t) be the one-parameter groups governing the time development of solutions of the Klein-Gordon equation, φ = m2φ, and the perturbed equation, φ = m2φ + V (x)φ, respectively. In a previous work the author obtained sufficient conditions on the potential V (x) which guaranteed the existence of the wave operators, W± := s limU(t)U0(t) as t →±∞. Here it is shown that if, in addition, the associated (Schrödinger) wave operators, W±s := s limei(m2I+V Δ)t ei(m2IΔ)t as t →∞, are complete and the Invariance Theorem is valid then the W± are also complete and are isometries. Finally, these results are used to show that the scattering operator, W+1W, is unitarily implemented in Fock space.

Mathematical Subject Classification
Primary: 81.47
Milestones
Received: 19 August 1968
Published: 1 October 1969
Authors
John Martin Chadam