In 1977 Avron and Herbt found a transformation for a free electron wave function that gives the time evolution of the electron wave function in an external uniform electric field. The transformation provides a powerful tool to construct a physically meaningful wave packet wave function that propagates under the influence of the electric field, without any approximation. However, in order to apply the Avron-Herbst transformation to a many-electron system, we have to take into account the statistics of the particles. The many-electron wave function must be anti-symmetric under permutaton of electrons. One of the most powerful ways to describe such an anti-symmetric wave function is the use of the second quantized electron field.
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