Vol. 1, No 3, 1996 pp.
204 - 218
UDC
530.1
p-ADIC HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY
G.S. Đorđević1, B. Dragović2
1 Department of Physics, University of Niš, P.O. Box 91, 18001 Niš
2 Institute of Physics, P.O. Box 57, 11001 Belgrade
Abstract.
Classical and quantum properties of the one-dimensional p-adic harmonic oscillator with time-dependent frequency are considered. A p-adic phase space is used to present classical evolution. The kernel of quantum evolution operator is found and the corresponding eigenvalue problem is formulated. Under definite conditions some vacuum states are obtained. As an illustration, examples of ω = ω0 and ω = ω0/(1 — at)2 are taken.
p-ADIČNI HARMONIJSKI OSCILATOR SA VREMENSKI ZAVISNOM FREKVENCIJOM
U radu je razmatran problem klasičnog i kvantnog harmonijskog oscilatora sa vremenski zavisnom frekvencijom nad poljem p-adičnih brojeva. Razmatrana je vremenska evolucija ovog sistema u skladu sa Vladimirov-Volovićevim formalizmom. Nađen je operator vremenske evolucije i njegovo jezgro, vakuumsko stanje, i ispitivane su mogućnosti njegove egzistencije i degeneracije. Posebno su razmatrani slučajevi ω = ω0 i ω = ω0/(1 — at)2.
