TheN-body problem with spin-orbit or Coulomb interactions

Autor:	Clasine van Winter, H. J. Brascamp
Rok vydání:	1968
Předmět:	Physics Continuous spectrum Statistical and Nonlinear Physics Fredholm integral equation Compact operator Fredholm theory Integral equation Many-body problem symbols.namesake Quantum mechanics symbols Hamiltonian (quantum mechanics) Complex plane Mathematical Physics
Zdroj:	Communications in Mathematical Physics. 11:19-55
ISSN:	1432-0916 0010-3616
DOI:	10.1007/bf01654300
Popis:	A study is made of the resolventR(λ) for a system ofn particles with spin-orbit coupling, an interaction which necessarily has a long range in momentum space. For short-range interactions, it has been known for several years thatR(λ) satisfies a Fredholm equation whose kernel is in the Schmidt-class. The corresponding spin-orbit kernel is not in the Schmidt-class, but it is shown that it does belong to a certain class of compact operators which is larger than the Schmidt-class. A modified Fredholm theory is presented which applies to all operators in this larger class. This enablesR(λ) to be found for all values of λ in the complex plane cut along the continuous spectrum of the Hamiltonian. It is shown that the modified Fredholm theory also holds for the Coulomb interaction.
Databáze:	OpenAIRE
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