The one‐dimensional Levinson’s theorem is derived and used to study zero‐energy resonances in a double‐potential system. The low energy behavior of time delay is also investigated. In particular, it is shown that the quantum mechanical time delay admits a classical lower bound, in the low energy limit, if the potential has no bound‐state solutions.

1.
N.
Levinson
,
Kgl. Danske Videnskab. Salskab. Mat. Fys. Medd.
25
,
9
(
1949
).
2.
R. G.
Newton
,
J. Math. Phys.
1
,
319
(
1960
).
3.
Ph. A.
Martin
,
Acta Phys. Austriaca Suppl.
23
,
159
(
1981
).
4.
R. G.
Newton
,
J. Math. Phys.
18
,
1348
(
1977
).
5.
J. M.
Jauch
,
Helv. Phys. Acta
30
,
143
(
1957
).
6.
N.
Poliatzky
,
Helv. Phys. Acta
66
,
241
(
1993
).
7.
L. D.
Faddeev
,
Am. Math. Soc. Transl.
2
,
139
(
1964
).
8.
P.
Deift
and
E.
Trubowitz
,
Commun. Pure Appl. Math.
32
,
121
(
1979
).
9.
R. G.
Newton
,
J. Math. Phys.
21
,
493
(
1980
).
10.
R. G.
Newton
,
J. Math. Phys.
24
,
2152
(
1983
).
11.
R. G.
Newton
,
J. Math. Phys.
25
,
2991
(
1984
).
12.
R.
Jackiw
and
G.
Woo
,
Phys. Rev. D
12
,
1643
(
1975
).
13.
T.
Aktosun
,
J. Math. Phys.
33
,
3865
(
1992
).
14.
M.
Sassoli de Bianchi
,
Helv. Phys. Acta
66
,
361
(
1993
).
15.
W.
van Dijk
and
K. A.
Kiers
,
Am. J. Phys.
60
,
520
(
1991
).
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