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Summary: Physica A 293 (2001) 189199
www.elsevier.com/locate/physa
Calculation of energy spectrum and eigenstates of
1D time-independent short-range potentials
Y. Ashkenazya;b;
, L.P. Horwitzc;d
aDepartment of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
bCenter for Polymer Studies and Department of Physics, Boston University, Boston,
MA 02215, USA
cInstitute for Advanced Study, Princeton, NJ, 08540, USA
dRaymond and Beverly Sackler Faculty of Exact Sciences School of Physics, Tel Aviv University,
Ramat Aviv 69978, Israel
Received 3 September 2000
Abstract
We show that it is possible to approximate 1D time-independent short-range potentials by a
sum of function potentials. By the use of transfer matrix techniques it is possible to calcu-
late the total transfer matrix as well as the S matrix which connects the incoming waves to
the outgoing waves. The transmission coe cient and the resonance states can be evaluated by
the function approximation. Using the same approach in potential wells, the energy spectrum,
as well as the eigenfunctions of the well, can be constructed. We examine the approximation,
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