Authors: Jean Louis Van Belle
We apply our realist interpretation of quantum mechanics to an analysis of the mechanics of electron propagation through a crystal and derive a formula for the effective mass of an electron which differs by a factor 2 from Feynman’s. We think this solves his rather weird remark on the relation between the effective and free-space mass of an electron, which says the effective mass turns out to be 2 to 20 times the free-space mass of the electron. Our calculations imply the effective mass equals the free-space mass in the absence of a potential barrier between successive atoms in an lattice, which is what is to be expected. We also find Feynman’s use of the small angle approximation for the argument of the wavefunction (so as to simplify the energy formula) is unjustified: the order of magnitude of the kb factor in the energy formula is one rad (radian), so that is too large for an small angle approximation. This remarkable result is surprising but makes sense because the reduced energy formula has no maximum, which contradicts the empirical reality of the conduction band in conductors as well as in semiconductors.
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