ISSN:
1573-0530
Keywords:
scattering matrix
;
stark
;
continuation
;
Schrödinger.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Quantum scattering in the presence of a constant electric field (‘Stark effect’) is considered. It is shown that the scattering matrix has a meromorphic continuation in the energy variable to the entire complex plane as an operator on L2(R n-1). The allowed potentials V form a general subclass of potentials that are short-range relative to the free Stark Hamiltonian: Roughly, the potential vanishes at infinity, and admits a decomposition $$V = V_\mathcal{A} + V_e$$ , where $$V_\mathcal{A}$$ is analytic in a sector with $$V_\mathcal{A} (x) = O(\left\langle {x_{} } \right\rangle ^{ - 1/2 - \varepsilon } )$$ , and $$V_e (x) = O({\text{e}}^{\mu x_1 } )$$ , for x1〈0 and some μ μ〉0. These potentials include the Coulomb potential. The wave operators used to define the scattering matrix are the two Hilbert space wave operators.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007565014305
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