Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/4672
Title: q-deformed and c-Deformed Harmonic Oscillators
Authors: Sogami, Ikuo S.
Koizumi, Kouzou
Mir-Kasimov, Rufat M.
Mir-Kasimov, Rufat M.
Izmir Institute of Technology. Mathematics
Keywords: Hamilton functions
c-deformed oscillators
q-deformed oscillators
Schrödinger equation
Issue Date: Oct-2003
Publisher: Yukawa Institute for Theoretical Physics
Source: Sogami, I. S., Koizumi, K., and Mir-Kasimov, R. M. (2003). q-deformed and c-Deformed Harmonic Oscillators. Progress of Theoretical Physics, 110(4), 819-840. doi:10.1143/PTP.110.819
Abstract: Hamilton functions of classical deformed oscillators (c-deformed oscillators) are derived from Hamiltonians of g-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 ℏ → 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 g-deformed oscillator carried out in the light of these findings for the c-deformed systems proves that the g-deformed systems are invariant under the same translation symmetries as the c-deformed systems and have propagating waves of the Bloch type
URI: http://doi.org/10.1143/PTP.110.819
http://hdl.handle.net/11147/4672
ISSN: 0033-068X
0033-068X
1347-4081
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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