Scattering theory of the Klein-Gordon equation in two Hilbert spaces with general and oscillating potentials

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5477017

Gelman, A

This dissertation considers three problems associated with the Klein-Gordon Equation: 1) conditions for the operator to be self-adjoint; 2) existence of the wave operator; and 3) completeness of the wave operator. These problems are considered for the operator with general and oscillating potentials. For problem 1, the work is based on the theory of forms extensions originated by K. Friederichs; and for problems 2 and 3, the abstract theory of scattering which originated in the work of Kato and Birman. The particular result which the author uses for problems 1 and 2 is the recent theorem proven by M. Schechter, in which he was able to relax requirements on J (no requirement for the bijectivity of J, and no reference to R(z), for example). Application of the methods described above to the Klein-Gordon operator allowed him to solve the three problems above for an unbounded operator J and also for the oscillating potential.

• Research Organization: Yeshiva Univ., New York (USA)
• OSTI ID: 5477017
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
HILBERT SPACE
KLEIN-GORDON EQUATION
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTUM OPERATORS
SCATTERING
SPACE
WAVE EQUATIONS