The inverse scattering problem of quantum theory |
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Authors: | B M Levitan |
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Institution: | 1. M. V. Lomonosov Moscow State University, USSR
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Abstract: | The inverse phase-type scattering problem for the boundary-value problem?y″+q(x)y=k 2 y (0?x<∞), (1)y′ (0)=hy (0) (2) is studied. It is shown that, for each function δ(k) satisfying the hypotheses of Levinson's theorem, there exists a problem (1)–(2) with h≠∞ and another problem (1)–(2) with h=∞ (i.e., with the boundary condition o (0)=0). The solvability condition for the Riemann-Hilbert problem is used more directly than has been done heretofore by others in deriving boundary condition (2). |
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