A time-dependent 2D harmonic oscillator in the presence of the Aharonov-Bohm effect with a time-dependent flux radius

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. Following the C values, the spectrum of the invariant operator is discrete ( C > 0) or continuous ( C <= 0). The time-dependent cross section for a free particle scattered by the AB potential is obtained.