We expand the scattering amplitude and the scattering matrix around the zero‐range limit, i.e., with point interactions, in the case when the potential has a finite number of wells. The lower‐order terms are largely independent of the shape of the potentials.
REFERENCES
1.
S. Albeverio, F. Gesztesy, H. Holden, and R. Ho/egh‐Krohn, Solvable Models in Quantum Mechanics (book in preparation).
2.
S.
Albeverio
, J. E.
Fenstad
, and R.
Ho/egh‐Krohn
, Trans. Am. Math. Soc.
252
, 275
(1979
).3.
A.
Grossmann
, R.
Ho/egh‐Krohn
, and M.
Mebkhout
, J. Math. Phys.
21
, 2376
(1980
), p. 106.4.
A.
Grossmann
, R.
Ho/egh‐Krohn
, and M.
Mebkhout
, Commun. Math. Phys.
77
, 87
(1980
).5.
6.
7.
8.
S.
Albeverio
, F.
Gesztesy
, and R.
Ho/egh‐Krohn
, Ann. Inst. H. Poincaré A
37
, 1
(1982
).9.
H.
Holden
, R.
Ho/egh‐Krohn
, and S.
Johannesen
, Adv. Appl. Math.
4
, 402
(1983
).10.
H. Holden, R. Ho/egh‐Krohn, and S. Johannesen, “The Short‐Range Expansion in Solid State,” to appear in Ann. Inst. H. Poincaré A.
11.
12.
13.
L. E. Thomas, “Scattering from point interaction,” in Lecture Notes in Physics, Vol. 130, edited by J. A. De Santo, A. W. Saenz, and W. W. Zachary (Springer‐Verlag, Berlin, 1980), pp. 159–162.
14.
15.
S.
Albeverio
, R.
Ho/egh‐Krohn
, and M.
Mebkhout
, J. Math. Phys.
25
, 1327
(1984
).16.
A. M. Berthier, Spectral Theory and Wave Operators for the Schrödinger Equation (Pitman, Boston, 1982).
17.
S. Albeverio, F. Gesztesy, R. Ho/egh‐Krohn, and W. Kirsch, “On point interactions in one dimension,” to appear in J. Operator Theory.
18.
H. Holden, “Konvergens mot punkt‐interaksjoner,” Cand. real, thesis, University of Oslo, 1981 (in Norwegian).
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