Multichannel stationary scattering theory in two-Hilbert space formulation
- 1 July 1973
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 14 (7) , 957-962
- https://doi.org/10.1063/1.1666422
Abstract
Two‐Hilbert space versions of the basic integral‐representation formulas for wave and transition operators are derived within the framework of time‐independent scattering theory. Multichannel scattering theory for state vectors as well as for statistical operators is presented in a two‐Hilbert space formulation to which these formulas become applicable. This formulation stays valid when long‐range interactions, for which renormalized wave operators exist, are present.Keywords
This publication has 8 references indexed in Scilit:
- Scattering Theory in Fock SpaceJournal of Mathematical Physics, 1972
- Riemann–Stieltjes Integration of Operator-Valued Functions with Respect to Vector-Valued Functions in Banach SpacesSIAM Journal on Mathematical Analysis, 1972
- Scattering problem for radial Schrödinger equation with a slowly decreasing potentialTheoretical and Mathematical Physics, 1972
- On time-dependent scattering theory for long-range interactionsIl Nuovo Cimento B (1971-1996), 1971
- Transport equations for dilute gases with internal degrees of freedomPhysica, 1971
- Quantum-mechanical scattering theory for short-range and Coulomb interactionsRocky Mountain Journal of Mathematics, 1971
- Scattering theory with two Hilbert spacesJournal of Functional Analysis, 1967
- Theory of Time-Dependent Scattering for Multichannel ProcessesPhysical Review B, 1956