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Citation - WoS: 10
Citation - Scopus: 9
Q-Deformed and C-Deformed Harmonic Oscillators
(Yukawa Institute for Theoretical Physics, 2003) Sogami, Ikuo S.; Koizumi, Kouzou; Mir-Kasimov, Rufat M.
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

Mathematics / Matematik