The uniqueness of the solution of the Schrodinger equation with discontinuous coefficients

Details The uniqueness of the solution of the Schrodinger equation with discontinuous coefficients The uniqueness of the solution of the Schrodinger equation with discontinuous coefficients

1998-11-30

arxiv.org/abs/math/9811176v1

Reviews in Mathematical Physics 10 (1998) 963-987

Mathematics

Spectral Theory

29 (twenty-nine) pages; no figures; to appear in Reviews of Mathematical Physics

Scientific paper

10.1142/S0129055X98000318

Consider the Schroeodinger equation: - Du(x) - l(x)u + s(x)u = 0, where D is the Laplacian, l(x) > 0 and s(x) is dominated by l(x). We shall extend the celebrated Kato's result on the asymptotic behavior of the solution to the case where l(x) has unbounded discontinuity. The result will be used to establish the limiting absorption principle for a class of reduced wave operators with discontinuous coefficients.

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