We reduce the two-body problem to the one-body problem in the general case of a deformed Heisenberg algebra leading to minimal length. Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain an analytical expression for the energy spectrum for partial cases of deformation function. The dependence of the energy spectrum on the center-of-mass momentum is found. For the special case of deformation function, which corresponds to a cutoff procedure in momentum space, it is shown that this dependence is more likely to be observed for identical particles.
REFERENCES
1.
H. S.
Snyder
, Phys. Rev.
71
, 38
(1947
).2.
D. J.
Gross
and P. F.
Mende
, Nucl. Phys. B
303
, 407
(1988
).3.
M.
Maggiore
, Phys. Lett. B
304
, 65
(1993
).4.
E.
Witten
, Phys. Today
49
(4
), 24
(1996
).5.
A.
Kempf
, J. Math. Phys.
35
, 4483
(1994
).6.
A.
Kempf
, G.
Mangano
, and R. B.
Mann
, Phys. Rev. D
52
, 1108
(1995
).7.
H.
Hinrichsen
and A.
Kempf
, J. Math. Phys.
37
, 2121
(1996
).8.
A.
Kempf
, J. Phys. A
30
, 2093
(1997
).9.
C.
Quesne
and V. M.
Tkachuk
, J. Phys. A
36
, 10373
(2003
).10.
C.
Quesne
and V. M.
Tkachuk
, J. Phys. A
37
, 10095
(2004
).11.
L. N.
Chang
, D.
Minic
, N.
Okamura
, and T.
Takeuchi
, Phys. Rev. D
65
, 125027
(2002
).12.
I.
Dadic
, L.
Jonke
, and S.
Meljanac
, Phys. Rev. D
67
, 087701
(2003
).13.
C.
Quesne
and V. M.
Tkachuk
, J. Phys. A
38
, 1747
(2005
).14.
C.
Quesne
and V. M.
Tkachuk
, J. Phys. A
39
, 10909
(2006
).15.
M. I.
Samar
and V.
M Tkachuk
, J. Math. Phys.
57
, 042102
(2016
).16.
M. I.
Samar
and V.
M Tkachuk
, J. Math. Phys.
57
, 082108
(2016
).17.
T. V.
Fityo
, I. O.
Vakarchuk
, and V. M.
Tkachuk
, J. Phys. A
39
, 2143
(2006
).18.
D.
Bouaziz
and M.
Bawin
, Phys. Rev. A
76
, 032112
(2007
).19.
D.
Bouaziz
and M.
Bawin
, Phys. Rev. A
78
, 032110
(2008
).20.
F.
Brau
, J. Phys. A
32
, 7691
(1999
).21.
S.
Benczik
, L. N.
Chang
, D.
Minic
, and T.
Takeuchi
, Phys. Rev. A
72
, 012104
(2005
).22.
M. M.
Stetsko
and V. M.
Tkachuk
, Phys. Rev. A
74
, 012101
(2006
).23.
M. M.
Stetsko
, Phys. Rev. A
74
, 062105
(2006
).24.
M. M.
Stetsko
and V. M.
Tkachuk
, Phys. Lett. A
372
, 5126
(2008
).25.
26.
27.
N.
Ferkous
, Phys. Rev. A
88
, 064101
(2013
).28.
S.
Pramanik
, S.
Ghosh
, and P.
Pal
, Phys. Rev. D
90
, 105027
(2014
).29.
F.
Buisseret
, Phys. Rev.
82
, 062102
(2010
).30.
C.
Quesne
and V. M.
Tkachuk
, Phys. Rev. A
81
, 012106
(2010
).31.
V. M.
Tkachuk
, Phys. Rev. A
86
, 062112
(2012
).32.
S.
Benczik
, L. N.
Chang
et al., Phys. Rev. D
66
, 026003
(2002
).33.
Kh. P.
Gnatenko
, Phys. Lett. A
377
, 3061
(2013
).34.
35.
Kh. P.
Gnatenko
and V. M.
Tkachuk
, Mod. Phys. Lett. A
31
(5
), 1650026
(2016
).36.
Kh. P.
Gnatenko
and V. M.
Tkachuk
, Phys. Lett. A
381
, 2463
(2017
).37.
T.
Maslowski
, A.
Nowicki
, and V. M.
Tkachuk
, J. Phys. A
45
, 075309
(2012
).© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.
