In this work we consider a quantum variation of the usual Aharonov-Bohm effect with two solenoids sufficiently close one to the other so that (external) electron cannot propagate between two solenoids but only around both solenoids. Here magnetic field (or classical vector potential of the electromagnetic field) acting at quantum propagating (external) electron represents the quantum mechanical average value or statistical mixture. It is obtained by wave function of single (internal, quantum propagating within some solenoid wire) electron (or homogeneous ensemble of such (internal) electrons) representing a quantum superposition with two practically non-interfering terms. All this implies that phase difference and interference shape translation of the quantum propagating (external) electron represent the quantum mechanical average value or statistical mixture. On the other hand we consider a classical analogy and variation of the usual Aharonov-Bohm effect in which Aharonov-Bohm solenoid is used for the primary coil inside secondary large coil in the remarkable classical Faraday experiment of the electromagnetic induction.
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