A STUDY OF THE WAVE-FUNCTION OF A PARTICLE STRIKING A CRYSTAL INTERFACE

The one-dimensional behavior of the wave function of a free particle s triking a crystal interface is studied. The free particle is described using a wave packet of plane waves, and the crystal is described usin g the Kronig-Penney model. It is found that when the wave packet is sp read over many unit cells, it behaves much like a free particle wave p acket striking a small step at the interface. The reflection and trans mission coefficients are derived and one finds that these coefficients do not contain the effective mass of the particle in the solid. This result is compared with a standard effective mass approach and it is f ound that the boundary conditions in the latter need to be modified to make it work. This model is useful in understanding the origin of the ''free electron'' picture in metals, as it describes from basic quant um mechanics, the exact wave function of the particle in the crystal. A computer visualization of the wave packet is presented.