The eigenstates of three particles moving in one dimension are classified according to the S3 plus parity group. The ordering of the ground state S3 band is given for a fairly general class of potentials. Sufficient conditions are given both for existence and nonexistence of bound states of a given symmetry.

1.
Yu. A.
Simonov
,
Sov. J. Nucl. Phys.
3
,
461
(
1966
).
Google Scholar
 
2.
R. L.
Hall
 and
H. R.
Post
,
Proc. Phys. Soc.
90
,
381
(
1967
).
Google Scholar
Crossref
Search ADS
 
3.
R. L.
Hall
,
Phys. Rev. C
20
,
1155
(
1979
).
Google Scholar
Crossref
Search ADS
 
4.
A. Weinstein and W. Stenger, Methods of Intermediate Problems for Eigenvalues (Academic, New York, 1972).
5.
W.
Hunziker
,
Helv. Pys. Acta
39
,
451
(
1966
).
Google Scholar
 
6.
B.
Simon
,
Helv. Phys. Acta
43
,
607
(
1970
).
Google Scholar
 
7.
F. A. B.
Coutinho
,
C. P.
Malta
, and
J.
Fernando Perez
,
Phys. Lett. A
97
,
242
(
1983
).
Google Scholar
Crossref
Search ADS
 
8.
C. P.
Malta
,
J.
Fernando Perez
, and
F. A. B.
Coutinho
, “
Bound states of N‐particles: a variational approach,” submitted to Nuovo Cimento; “Sufficient conditions for the existence of bound states of N‐particles with attractive potentials
,”
Phys. Lett. A
100
,
460
(
1984
).
Google Scholar
 
9.
F.
Calogero
,
J. Math. Phys.
6
,
161
(
1965
).
Google Scholar
Crossref
Search ADS
 
10.
I.
Sigal
,
Commun. Math. Phys.
48
,
137
(
1976
).
Google Scholar
Crossref
Search ADS
 
This content is only available via PDF.
© 1984 American Institute of Physics.
1984
American Institute of Physics
You do not currently have access to this content.