Schrödinger operators with a nonspherical radiation condition

Academic Article

Abstract

  • The Schrödinger operators with potentials p(x) which do not necessarily converge to a constant at infinity will be discussed. The potential p(x) = x1/|x|, x = (x1, x2,…, xn) ∈ Rn, is an example. The radiation condition associated with such Schródinger operators is shown to have the form ∇u-i√λ(∇R)u = small at infinity, where R = R(x, λ) is a solution of the eikonal equation |∇R|2 = 1 - p(x)/λ. This radiation condition is "nonspherical" in the sense that ∇R is not proportional to the vector x = x/|x| in general. The limiting absorption principle will be obtained using a priori estimates for the radiation condition. © 1987 by Pacific Journal of Mathematics.
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    Author List

  • Saito Y
  • Start Page

  • 331
  • End Page

  • 359
  • Volume

  • 126
  • Issue

  • 2