We present an exact solution of the one-dimensional Bosonic oscillator for spin 1 and spin 0, in the momentum space with the presence of minimal length uncertainty, the energy eigenvalues, and eigenfunctions are then determined for both cases.
REFERENCES
1.
G.
Veneziano
, Europhys. Lett.
2
, 199
(1986
);D.
Amati
, M.
Ciafaloni
, and G.
Veneziano
, Phys. Lett. B
197
, 81
(1987
);K.
Konishi
, G.
Paffuti
, and P.
Provero
, Phys. Lett. B
234
, 276
(1990
);M.
Kato
, Phys. Lett. B
245
, 43
(1990
);R.
Guida
, K.
Konishi
, and P.
Provero
, Mod. Phys. Lett. A
6
, 1487
(1991
).2.
D. J.
Gross
and P. F.
Mende
, Nucl. Phys. B
303
, 407
(1988
).3.
L. J.
Garay
, Int. J. Mod. Phys. A
10
, 145
(1995
).4.
S.
Capozziello
, G.
Lambiase
, and G.
Scarpetta
, Int. J. Theor. Phys.
39
, 15
(2000
).5.
F.
Scardigli
, Phys. Lett. B
452
, 39
(1999
);F.
Scardigli
and R.
Casadio
, Class. Quantum Grav.
20
, 3915
(2003
).6.
A.
Kempf
, J. Math. Phys.
35
, 4483
(1994
);A.
Kempf
, G.
Mangano
, and R. B.
Mann
, Phys. Rev. D
52
, 1108
(1995
);A.
Kempf
, J. Phys. A
30
, 2093
(1997
);H.
Hinrichsen
and A.
Kempf
, J. Math. Phys.
37
, 2121
(1996
);L. N.
Chang
, D.
Minic
, N.
Okamura
, and T.
Takeuchi
, Phys. Rev. D
65
, 125027
(2002
);L. N.
Chang
, D.
Minic
, N.
Okamura
, and T.
Takeuchi
, Phys. Rev. D
65
, 125028
(2002
);S.
Benczik
, L. N.
Chang
, D.
Minic
, N.
Okamura
, S.
Rayyan
, and T.
Takeuchi
, Phys. Rev. D
66
, 026003
(2002
);K.
Nozari
, Phys. Lett. B
629
, 41
(2005
);D.
Spector
, J. Math. Phys.
49
, 082101
(2008
).7.
J.
Slawny
, J. Math. Phys.
48
, 053515
(2007
);Kh.
Nouicer
, J. Math. Phys.
48
, 112104
(2007
);F.
Brau
, J. Phys. A
32
, 7691
(1999
);S.
Benczik
, L. N.
Chang
, D.
Minic
, and T.
Takeuchi
, Phys. Rev. A
72
, 012104
(2005
).8.
D.
Bouaziz
and M.
Bawin
, Phys. Rev. A
76
, 032112
(2007
).9.
K.
Nozari
and T.
Azizi
, Gen. Relativ. Gravit.
38
, 735
(2006
).10.
Kh.
Nouicer
, J. Math. Phys.
47
, 122102
(2006
).11.
M.
Merad
and F.
Falek
, Phys. Scr.
79
, 015010
(2009
).12.
13.
J.
Sadeghi
, J. Math. Phys.
48
, 113508
(2007
);C.
Quesne
and V. M.
Tkachuk
, J. Phys. A
38
, 1747
(2005
);K.
Nouicer
, J. Phys. A
39
, 5125
(2006
).14.
J.
Beckers
, N.
Debergha
, and A. G.
Nikitin
, J. Math. Phys.
33
, 3387
(1992
);M.
Bednar
, J.
Ndimubandi
, and A. G.
Nikitin
, Can. J. Phys.
75
, 283
(1997
).15.
Y.
Nedjadi
and R. C.
Barrett
, J. Phys. A
27
, 4301
(1994
);Y.
Nedjadi
and R. C.
Barrett
, J. Phys. A
31
, 6717
(1998
);Y.
Nedjadi
and R. C.
Barrett
, J. Math. Phys.
35
, 4517
(1994
);Y.
Nedjadi
, S.
Ait-Tahar
, and R. C.
Barrett
, J. Phys. A
31
, 3867
(1998
).16.
17.
18.
I.
Boztosun
, M.
Karakoc
, F.
Yasuk
, and A.
Durmus
, J. Math. Phys.
47
, 062301
(2006
).19.
M.
Moshinsky
and A.
Szczepaniak
, J. Phys. A
22
, L817
(1989
).20.
R. Y.
Duffin
, Phys. Rev.
54
, 1114
(1938
);N.
Kemmer
, Proc. R. Soc. London, Ser. A
173
, 91
(1939
);G.
Petiau
, Academie Royale de Belgique, Classe des Sciences, Memoires. Collection 16.21.
L.
Chetouani
, M.
Merad
, T.
Boudjedaa
, and A.
Lecheheb
, Int. J. Theor. Phys.
43
, 1147
(2004
);M.
Merad
, Int. J. Theor. Phys.
46
, 2105
(2007
;M.
Merad
, H.
Bada
, and A.
Lecheheb
, Czech. J. Phys.
56
, 765
(2006
);M.
Merad
and S.
Bensaid
, J. Math. Phys.
48
, 073515
(2007
)22.
N.
Debergh
, J.
Ndimubandi
, D.
Strivay
, Z. Phys. C-Part. Fields
56
, 421
(1992
).23.
M.
de Montigny
, F. C.
Khanna
, A. E.
Santana
, E. S.
Santos
, and J. D. M.
Vianna
, J. Phys. A
33
, L273
(2000
).24.
M.
Moreno
and A. J.
Zentella
, J. Phys. A
22
, L821
(1989
);J.
Bentez
, R. P.
Martinez y Romero
, H. N.
Nunez-Yepez
, and A. L.
Salas-Brito
, Phys. Rev. Lett.
64
, 1643
(1990
);
[PubMed]
R. P.
Martinez y Romero
, H. N.
Nunez-Yepez
, and A. L.
Salas-Brito
, Eur. J. Phys.
16
, 135
(1995
).25.
26.
27.
L.
Chetouani
, M.
Merad
, T.
Boudjedaa
, and A.
Lecheheb
, Acta Phys. Slov.
55
, 379
(2005
).28.
M.
Falek
and M.
Merad
, Commun. Theor. Phys.
50
, 587
(2008
).29.
R.
Guertin
and T. L.
Wilson
, Phys. Rev. D
15
, 1518
(1977
).30.
I. S.
Gradshteyn
and I. M.
Ryzhik
, Tables of Integrals, Series and Products
(Academic
, New York
, 1980
).© 2009 American Institute of Physics.
2009
American Institute of Physics
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