ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract: For operators with a discrete spectrum, {λ j 2}, the counting function of λ j 's, N (λ), trivially satisfies N ( λ+δ ) −N ( λ−δ ) =∑ j δλ j ((λ−δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λ j ∈ℂ+, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that where ωℂ+ is the harmonic measure of the upper of half plane and δ can be taken dependent on λ. This provides a precise high energy version of the Breit–Wigner approximation, and relates the properties of s (λ) to the distribution of resonances close to the real axis.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002200050648
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