Schr{umlt o}dinger-like equation for a nonrelativistic electron in a photon field of arbitrary intensity
- Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
- Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540 (United States)
The Schr{umlt o}dinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schr{umlt o}dinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The {open_quotes}eigenvalue{close_quotes} in the present equation is an operator in a Cartan subalgebra. An approximation consistent with the nonrelativistic energy level derived from its relativistic value replaces the eigenvalue operator by an ordinary number, recovering the Schr{umlt o}dinger eigenvalue equation used in the formal scattering formalism. The Schr{umlt o}dinger-like equation for the multimode case is also presented. {copyright} {ital 1998} {ital The American Physical Society}
- OSTI ID:
- 638780
- Journal Information:
- Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 58; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quantum lattice-gas model for the many-particle Schr{umlt o}dinger equation in d dimensions
On Schr{umlt o}dinger equations with concentrated nonlinearities