Abstract
Using a unitary transformation, the Dirac equation with a time-dependent linear potential is transformed into a Schrödinger equation for a particle moving in an effective external magnetic field, which can be solved by the Lewis–Riesenfeld invariant theory. The wavefunction is written in a complete form. It is also shown that in the non-relativistic limit, matrix elements of the velocity operator go to the classical velocity when there is an arbitrary external potential and a magnetic field.
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