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FIZIKA B 13 (2004) 4, 691-698
 
NON-COMPACT GROUP SU(1,1) OF A FREE PARTICLE IN THE SYMMETRIC
DOUBLE-WELL POTENTIAL FIELD
J. SADEGHIa,b,1, M. R. PAHLAVNIb,2 and A. DARYAIEb,3
aInstitute for Studies in Theoretical Physics and Mathematics
(IPM), P. O. Box 19395-5531, Tehran, Iran
bSciences Faculty, Department of Physics, Mazandaran University, P. O. Box
47415-416, Babolsar, Iran
E-mail addresses: 1pouriya@ipm.ir, 2m.pahlavani@umz.ac.ir , 3afshindaryaie@yahoo.com
Received 24 November 2004; Accepted 13 December 2004
Online 2 February 2005
We analyze the equation of motion for a particle in the double-well potential. We find
the symmetries through Lie's method of group analysis. In the corresponding quantum
mechanical case, the method of spectrum-generating su(1,1) algebra is used to find energy
levels as solutions of the Schrödinger equation with double-well potential, without
solving the equation explicitly. Finally, we discuss the symmetry version of the
double-well potential with the vector-field formalism.
PACS numbers: 02.20.Sv, 02.20.Qs, 02.20.Hj, 03.65.-w, 03.65.Fd
UDC 538.915
Keywords: double-well potential, Lie algebra, energy spectrum, vector field, symmetry
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