 9841 Teufel S., Duerr D., MuenchBerndl K.
 The FluxAcrossSurfaces Theorem for Short Range Potentials and Wave Functions without Energy Cutoffs
(82K, LATeX 2e)
Jan 30, 98

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Abstract. The quantum probability flux of a particle integrated over time and a distant
surface gives the probability for the particle crossing that surface at some
time. The relation between these crossing probabilities and the usual formula
for the scattering cross section is provided by the fluxacrosssurfaces
theorem, which was conjectured by Combes, Newton and Shtokhamer in Phys.Rev.D
11, 366372 (1975). We prove the fluxacrosssurfaces theorem for short range
potentials and wave functions without energy cutoffs. The proof is based on the
free fluxacrosssurfaces theorem (Daumer et.al. in Lett. in Math. Phys. 38,
103116 (1996)), and on smoothness properties of generalized eigenfunctions:
It is shown that if the potential V(x) decays like x^{g} at infinity with
g > n then the generalized eigenfunctions of the corresponding Hamiltonian
\frac{1}{2}\Delta + V are n2 times continuously differentiable with respect
to the momentum variable.
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