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Prog. Theor. Phys. Vol. 110 No. 4 (2003) pp. 819-840

[ Full Text PDF : FREE ACCESS (729K) ]

q-Deformed and c-Deformed Harmonic Oscillators

Ikuo S. Sogami1,* Kouzou Koizumi1,** and Rufat M. Mir-Kasimov2,***

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
and
Department of Mathematics, Izmir Institute of High Technology, 35437, Urla-Izmir, Turkey

(Received May 7, 2003)

Abstract:

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.


URL : http://ptp.ipap.jp/link?PTP/110/819/
DOI : 10.1143/PTP.110.819


*E-mail: sogami@cc.kyoto-su.ac.jp
**E-mail: kkoizumi@cc.kyoto-su.ac.jp
***E-mail: mirkr@thsun1.jinr.ru

[ Full Text PDF : FREE ACCESS (729K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 113 No. 3 (2005) pp. 645-656 :
    q-Deformed Bi-Local Fields
    Shigefumi Naka, Haruki Toyoda and Aiko Kimishima
  2. 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

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