Prog. Theor. Phys. Vol. 110 No. 4 (2003) pp. 819-840
q-Deformed and c-Deformed Harmonic Oscillators
1Department of Physics, Kyoto Sangyo University,
Kyoto 603-8555, Japan
2Bogoliubov Laboratory of Theoretical Physics, Joint Institute for
Nuclear Research, Dubna, Moscow Region, 141980, Russia
Department of Mathematics, Izmir Institute of High Technology, 35437,
(Received May 7, 2003)
Hamilton functions of classical deformed oscillators (c-deformed
oscillators) are derived from Hamiltonians of q-deformed oscillators
of the Macfarlane and Dubna types. A new scale parameter, lq,
with the dimension of length, is introduced to relate a dimensionless
parameter characterizing the deformation with the natural length of
the harmonic oscillator. Contraction from q-deformed oscillators to
c-deformed oscillators is accomplished by keeping lq finite while
taking the limit \hbar→0. The c-deformed Hamilton
functions for both types of oscillators are found to be invariant
under discrete translations: the step of the translation for the
Dubna oscillator is half of that for the Macfarlane oscillator.
The c-deformed oscillator of the Macfarlane type has propagating
solutions in addition to localized ones. Reinvestigation of the
q-deformed oscillator carried out in the light of these findings
for the c-deformed systems proves that the q-deformed systems
are invariant under the same translation symmetries as the
c-deformed systems and have propagating waves of the Bloch type.
DOI : 10.1143/PTP.110.819
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Citing Article(s) :
Progress of Theoretical Physics Vol. 113 No. 3 (2005) pp. 645-656
q-Deformed Bi-Local Fields
Shigefumi Naka, Haruki Toyoda and Aiko Kimishima
Progress of Theoretical Physics Vol. 117 No. 4 (2007) pp. 589-600
Localized and Non-Localized Solutions of q-Deformed Oscillators
Kozo Koizumi and Ikuo S. Sogami