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https://hdl.handle.net/11147/4672
Title: | Q-Deformed and C-Deformed Harmonic Oscillators | Authors: | Sogami, Ikuo S. Koizumi, Kouzou Mir-Kasimov, Rufat M. |
Keywords: | Hamilton functions c-deformed oscillators q-deformed oscillators Schrödinger equation |
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 1347-4081 0033-068X |
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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