Title: Electron conduction in solid state via time varying wavevectors,
Abstract: In this paper, we study electron wavepacket dynamics in electric and magnetic
fields. We rigorously derive the semiclassical equations of electron dynamics
in electric and magnetic fields. We do it both for free electron and electron
in a periodic potential. We do this by introducing time varying wavevectors
$k(t)$. In the presence of magnetic field, our wavepacket reproduces the
classical cyclotron orbits once the origin of the Schröedinger equation is
correctly chosen to be center of cyclotron orbit. In the presence of both
electric and magnetic fields, our equations for wavepacket dynamics differ from
classical Lorentz force equations. We show that in a periodic potential, on
application of electric field, the electron wave function adiabatically follows
the wavefunction of a time varying Bloch wavevector $k(t)$, with its energies
suitably shifted with time. We derive the effective mass equation and discuss
conduction in conductors and insulators.