Sogami, Ikuo S.Koizumi, KouzouMir-Kasimov, Rufat M.2016-05-272016-05-272003Sogami, 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.110.8190033-068X1347-40810033-068Xhttp://doi.org/10.1143/PTP.110.819https://hdl.handle.net/11147/4672Hamilton 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 typeeninfo:eu-repo/semantics/openAccessHamilton functionsc-deformed oscillatorsq-deformed oscillatorsSchrödinger equationArticle2-s2.0-034627153910.1143/PTP.110.81910.1143/PTP.110.819