Abstract
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.
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