An elementary calculation for a charged particle in a time-dependent m
agnetic field is carried out using a semiclassical method. We consider
an external magnetic field pointing along the (z) over cap-axis and c
hoose the gauge vector potential such that A(x, t) = -B(t)y (i) over c
ap. Using the path integral formulation, we obtain the propagator of t
his system with an auxiliary condition as the classical solution.