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International Journal of Theoretical Physics

Time-Dependent 2D Harmonic Oscillator in Presence of the Aharanov-Bohm Effect

Yacine Bouguerra, Mustapha Maamache, Abdelhafid Bounames

Published Jun 26, 2006• 11 citations
Publisher
DOI
10.1007/s10773-006-9145-9

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The quantum states of the 2D time-dependent harmonic oscillator with the Aharonov–Bohm (AB) effect are investigated by employing the invariant operator method and the unitary transformation approach. The time-dependent radius case of a solenoid is treated. The qualitative properties of the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation, i.e. C>0, C=0 and C 0) or continuous (C≤0). The time-dependent cross section for a free particle scattered by the AB potential is obtained.