  The Landau levels of scalar QED undergo continuous transitions under a
homogeneous, time-dependent magnetic field. We analytically formulate the
Klein-Gordon equation for a charged spinless scalar as a Cauchy initial value
problem in the two-component first order formalism and then put forth a measure
that classifies the quantum motions into the adiabatic change, the nonadiabatic
change, and the sudden change. We find the exact quantum motion and calculate
the pair-production rate when the magnetic field suddenly changes as a step
function.
