Asymptotic Wave Vector and Nonrelativistic Perturbation Theory

Journal Article · Tue Jan 01 04:00:00 EST 1963 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1704042· OSTI ID:4632079

Teitler, S.

The dual nature of perturbations in causing both transitions and persistent effects is investigated. A wave vector initially represented in terms of a set of unperturbed eigenvectors is subjected to a nondissipative perturbation. After a long time, it is assumed that this unperturbed wave vector evolves into an asymptotic wave vector in which both persistent and transition effects are present. These two effects are considered separately and the asymptotic wave vector is formally expressed as an expansion in terms of asymptotically stationary states. A time-operator form of nonrelativistic perturbation theory which formally is very similar to the resolvent formalism is presented. In a manner similar to the resolvent formalism, diagonal and nondiagonal contributions to the development operator are considered separately. A further classification of the development operator into asymptotic and nonasymptotic parts is made. This latter form is used to obtain an explicit form for the asymptotic wave vector, and the asymptotically stationary states are identified.

• Research Organization: Naval Research Lab., Washington, D.C.
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-036840
• OSTI ID: 4632079
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 4; ISSN JMAPAQ; ISSN 0022-2488
• Publisher: American Institute of Physics (AIP)
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVECTORS
PERTURBATION THEORY
TRANSIENTS
VECTORS
WAVE MECHANICS