Reflectionless Approximations to Potentials With Band Structure

Rosner, Jonathan L.

doi:10.1016/0003-4916(90)90243-H

Reflectionless Approximations to Potentials With Band Structure

Jonathan L. Rosner
(
- Chicago U., EFI and
- Chicago U.
)

Aug, 1989

43 pages

Published in:

Annals Phys. 200 (1990) 101

DOI:

10.1016/0003-4916(90)90243-H

Report number:

EFI-89-32

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Abstract: (Elsevier)

Inverse scattering methods are used to construct approximations to one-dimensional periodic potentials with a known band structure. By nature of the construction, these potentials give rise to reflectionless continuum scattering. A partial differential equation describing the problem and a numerical method for its solution are given. Some simple examples illustrate the degree to which the approximations correctly represent known potentials. Possible applications of our methods are noted.

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