The Friedrichs model with one discrete state coupled to more than one continuum is studied. The exact eigenstates for the full Hamiltonian can be solved explicitly. The discrete state is found to generate more than one virtual state pole or more than one pair of resonance poles in different Riemann sheets in different situations. The form factors could also generate new states on different sheets. All these states can appear in the generalized completeness relation.

1.
K. A.
Olive
 et al (Particle Data Group),
Chin. Phys. C
38
,
090001
(
2014
).
2.
S.
Godfrey
and
N.
Isgur
,
Phys. Rev. D
32
,
189
(
1985
).
3.
M. R.
Pennington
and
D. J.
Wilson
,
Phys. Rev. D
76
,
077502
(
2007
); e-print arXiv:0704.3384 [hep-ph].
4.
S.
Coito
,
G.
Rupp
, and
E.
van Beveren
,
Eur. Phys. J. C
73
,
2351
(
2013
); e-print arXiv:1212.0648 [hep-ph].
5.
Z.-Y.
Zhou
and
Z.
Xiao
,
Eur. Phys. J. A
50
,
165
(
2014
); e-print arXiv:1309.1949 [hep-ph].
6.
B.-Q.
Li
and
K.-T.
Chao
,
Phys. Rev. D
79
,
094004
(
2009
); e-print arXiv:0903.5506 [hep-ph].
7.
Z.
Xiao
and
H. Q.
Zheng
,
Nucl. Phys. A
695
,
273
(
2001
); e-print arXiv:hep-ph/0011260 [hep-ph].
8.
H. Q.
Zheng
,
Z. Y.
Zhou
,
G. Y.
Qin
,
Z.
Xiao
,
J. J.
Wang
, and
N.
Wu
,
Nucl. Phys. A
733
,
235
(
2004
); e-print arXiv:hep-ph/0310293 [hep-ph].
9.
Z.-Y.
Zhou
and
Z.
Xiao
,
Phys. Rev. D
83
,
014010
(
2011
); e-print arXiv:1007.2072 [hep-ph].
10.
Z.-Y.
Zhou
and
Z.
Xiao
,
Phys. Rev. D
84
,
034023
(
2011
); e-print arXiv:1105.6025 [hep-ph].
11.
K. O.
Friedrichs
,
Commun. Pure Appl. Math.
1
,
361
(
1948
).
12.
L.
Horwitz
and
J.
Marchand
,
Rocky Mt. J. Math.
1
,
225
(
1971
).
13.
I. E.
Antoniou
and
I.
Prigogine
,
Phys. A
192
,
443
(
1993
).
14.
A.
Bohm
and
M.
Gadella
, in
Dirac Kets, Gamow Vectors and Gel’fand Triplets
, Lecture Notes in Physics, edited by
A.
Bohm
and
J. D.
Dollard
(
Springer Berlin Heidelberg
,
1989
), Vol. 348, ISBN: 978-3-540-51916-4 (Print) 978-3-540-46859-2 (Online).
15.
O.
Civitarese
and
M.
Gadella
,
Phys. Rep.
396
,
41
(
2004
).
16.
Z.
Xiao
and
Z.-Y.
Zhou
,
Phys. Rev. D
94
,
076006
(
2016
); e-print arXiv:1608.00468 [hep-ph].
17.
A. K.
Likhoded
and
G. P.
Pronko
,
Int. J. Theor. Phys.
36
,
2335
(
1997
).
18.
G.
Stey
and
R.
Gibberd
,
Physica
60
,
1
(
1972
).
19.
T. K.
Bailey
and
W. C.
Schieve
,
Il Nuovo Cimento A
47
,
231
(
1978
).
20.
G.
Ordonez
and
S.
Kim
,
Phys. Rev. A
70
,
032702
(
2004
).
21.
I.
Antoniou
,
E.
Karpov
,
G.
Pronko
, and
E.
Yarevsky
,
Int. J. Theor. Phys.
42
,
2403
(
2003
).
22.
M.
Gadella
and
G.
Pronko
,
Fortschr. Phys.
59
,
795
(
2011
); e-print arXiv:1106.5782 [math-ph].
23.
O.
Civitarese
and
M.
Gadella
,
Int. J. Mod. Phys. E
15
,
1273
(
2006
); e-print arXiv:nucl-th/0703090 [nucl-th].
24.
O.
Civitarese
,
M.
Gadella
, and
G. P.
Pronko
,
Int. J. Mod. Phys. E
16
,
169
(
2007
); e-print arXiv:nucl-th/0703091 [nucl-th].
25.
T.
Petrosky
,
I.
Prigogine
, and
S.
Tasaki
,
Phys. A
173
,
175
(
1991
).
26.
D.
Morgan
,
Nucl. Phys. A
543
,
632
(
1992
).
27.
R. J.
Eden
and
J. R.
Taylor
,
Phys. Rev.
133
,
B1575
(
1964
).
28.
Z.-Y.
Zhou
and
Z.
Xiao
,
Phys. Rev. D
92
,
094024
(
2015
); e-print arXiv:1505.05761 [hep-ph].
29.
Z.-Y.
Zhou
and
Z.
Xiao
, e-print arXiv:1704.04438 [hep-ph] (
2017
).
30.
T. D.
Lee
,
Phys. Rev.
95
,
1329
(
1954
).
31.
I. E.
Antoniou
,
M.
Gadella
,
J.
Mateo
, and
G. P.
Pronko
,
J. Phys. A
36
,
12109
(
2003
).
32.
E.
Karpov
,
I.
Prigogine
,
T.
Petrosky
, and
G.
Pronko
,
J. Math. Phys.
41
,
118
(
2000
).
33.
U.
Fano
,
Phys. Rev.
124
,
1866
(
1961
).
34.
P. W.
Anderson
,
Phys. Rev.
124
,
41
(
1961
).
35.
G.
Duerinckx
,
J. Phys. A: Math. Gen.
16
,
L289
(
1983
).
36.
M.
Miyamoto
,
Phys. Rev. A
72
,
063405
(
2005
).
37.
S.
Longhi
,
Eur. Phys. J. B
57
,
45
(
2007
).
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