Scattering in one dimension: The coupled Schr{umlt o}dinger equation, threshold behaviour and Levinson{close_quote}s theorem
- Department of Physics, University of British Columbia, Vancouver, British Columbia, V6T 1Z1 (CANADA)
- Redeemer College, Ancaster, Ontario, L9G 3N6 (CANADA)
We formulate scattering in one dimension due to the coupled Schr{umlt o}dinger equation in terms of the {ital S} matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson{close_quote}s theorem is seen to have the form {eta}(0)={pi}({ital n}{sub {ital b}}+1/2{ital n}{minus}1/2{ital N}), where {eta}(0) is the phase of the {ital S} matrix at zero energy, {ital n}{sub {ital b}} the number of bound states with nonzero binding energy, {ital n} the number of half-bound states, and {ital N} the number of coupled equations. In view of the effects due to the half-bound states, the threshold behaviour of the scattering amplitudes is investigated in general, and is also illustrated by means of particular potential models. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 397452
- Journal Information:
- Journal of Mathematical Physics, Vol. 37, Issue 12; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
Similar Records
Schr{umlt o}dinger-like equation for a nonrelativistic electron in a photon field of arbitrary intensity
Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schr{umlt o}dinger-type equations