Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
38 (1997), S. 3497-3507
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Let V(x) denote a potential in the one-dimensional Schrödinger equation, without bound states, for which (1) V(x)=0 for x〈0 and (2) V(x) is piecewise continuous with adequate decay as x goes to infinity. We are interested in the problem of determining V given the reflectivity r(k)=|R(k)|, where R is the usual left-hand reflection coefficient. For very special classes of potentials it is known that r determines V uniquely. Here we show that under much more general (although still restrictive) assumptions, the location and magnitude of discontinuities of V can be determined from r. The nature of the restrictions is related to the behavior of R(k) for k in the upper half of the complex plane. © 1997 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531865
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