The system of two Q-deformed oscillators coupled so that the total Hamiltonian has the suQ(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the Q-oscillators by deformed anharmonic oscillators. The generalization to n oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.

1.
V. G. Drinfeld, in Proceedings of the International Congress of Mathematicians, edited by A. M. Gleason (American Mathematical Society, Providence, RI, 1986), p. 798.
2.
M.
Jimbo
,
Lett. Math. Phys.
11
,
247
(
1986
).
3.
E. Abe, Hopf Algebras (Cambridge University Press, Cambridge, 1977).
4.
M. Jimbo, in Braid Group, Knot Theory and Statistical Mechanics, edited by C. N. Yang and M. L. Ge (World Scientific, Singapore, 1989), p. 111.
5.
L. C.
Biedenharn
,
J. Phys. A
22
,
L873
(
1989
).
6.
A. J.
Macfarlane
,
J. Phys. A
22
,
4581
(
1989
).
7.
C. P.
Sun
and
H. C.
Fu
,
J. Phys. A
22
,
L983
(
1989
).
8.
D.
Bonatsos
,
P. P.
Raychev
,
R. P.
Roussev
, and
Yu. F.
Smirnov
,
Chem. Phys. Lett.
175
,
300
(
1990
).
9.
Z.
Chang
and
H.
Yan
,
Phys. Lett. A
154
,
254
(
1991
).
10.
Z.
Chang
,
H. Y.
Guo
, and
H.
Yan
,
Commun. Theor. Phys.
17
,
183
(
1992
).
11.
D.
Bonatsos
and
C.
Daskaloyannis
,
Phys. Rev. A
46
,
75
(
1991
).
12.
D.
Bonatsos
,
C.
Daskaloyannis
, and
K.
Kokkotas
,
J. Math. Phys.
33
,
2958
(
1992
).
13.
Y.
Alhassid
,
F.
Gürsey
, and
F.
Iachello
,
Ann. Phys.
148
,
346
(
1983
).
14.
P. P.
Raychev
,
Adv. Quantum Chem.
26
,
239
(
1995
).
15.
G. Herzberg, Molecular Spectra and Molecular Structure Vol. III, Electronic Spectra and Electronic Structure of Polyatomic Molecules (Van Nostrand, Toronto, 1979).
16.
B. T.
Darling
and
D. M.
Dennison
,
Phys. Rev.
57
,
128
(
1940
).
17.
M. E.
Kellman
,
J. Chem. Phys.
81
,
389
(
1984
).
18.
M. E.
Kellman
,
Chem. Phys. Lett.
113
,
489
(
1985
).
19.
M. E.
Kellman
,
J. Chem. Phys.
83
,
3843
(
1985
).
20.
F.
Iachello
and
S.
Oss
,
Phys. Rev. Lett.
66
,
2976
(
1991
).
21.
F.
Iachello
and
S.
Oss
,
Chem. Phys. Lett.
187
,
500
(
1991
).
22.
F.
Iachello
and
S.
Oss
,
J. Mol. Spectrosc.
153
,
225
(
1992
).
23.
F.
Iachello
and
S.
Oss
,
J. Chem. Phys.
99
,
7337
(
1993
).
24.
F.
Iachello
and
R. D.
Levine
,
J. Chem. Phys.
77
,
3046
(
1982
).
25.
O. S.
van Roosmalen
,
F.
Iachello
,
R. D.
Levine
, and
A. E. L.
Dieperink
,
J. Chem. Phys.
79
,
2515
(
1983
).
26.
P. P. Kulish, in Group Theoretical Methods in Physics, edited by V. V. Dodonov and V. I. Man’ko (Springer, Berlin, 1991), p. 195.
27.
E. G.
Floratos
,
J. Phys. A
24
,
4739
(
1991
).
28.
C. P.
Sun
,
X. F.
Liu
,
J. F.
Lu
, and
M. L.
Ge
,
J. Phys. A
25
,
L35
(
1992
).
29.
S. Flügge, Practical Quantum Mechanics (Springer, Berlin, 1974).
30.
M.
Arik
and
D. D.
Coon
,
J. Math. Phys.
17
,
524
(
1976
).
31.
M. V.
Kuryshkin
,
Ann. Fondation Louis de Broglie
5
,
111
(
1980
).
32.
A. Jannussis, in Hadronic Mechanics and Non-potential Interactions, edited by H. C. Muyng (Nova Science, Commack, NY, 1991).
33.
P. P.
Kulish
and
E. V.
Damaskinsky
,
J. Phys. A
23
,
L415
(
1990
).
34.
R.
Chakrabarti
and
R.
Jagannathan
,
J. Phys. A
24
,
L711
(
1991
).
35.
I. L.
Cooper
,
Chem. Phys.
112
,
67
(
1987
).
36.
Th. Ioannidou, Diploma thesis, University of Thessaloniki, 1993.
37.
D.
Bonatsos
and
C.
Daskaloyannis
,
Chem. Phys. Lett.
203
,
150
(
1993
).
38.
M. E.
Kellman
,
Annu. Rev. Phys. Chem.
46
,
395
(
1995
).
39.
F.
Iachello
,
S.
Oss
, and
R.
Lemus
,
J. Mol. Spectrosc.
149
,
132
(
1991
).
40.
D.
Bonatsos
and
C.
Daskaloyannis
,
Phys. Rev. A
48
,
3611
(
1993
).
41.
O. S.
van Roosmalen
,
I.
Benjamin
, and
R. D.
Levine
,
J. Chem. Phys.
81
,
5986
(
1984
).
This content is only available via PDF.
You do not currently have access to this content.