Dirac Equation for Electron Channeling
It is well-known that the electron’s spin can be neglected in channeling. One may approximate the Dirac equation by an effective Schrödinger equation governing the motion transverse to a string or a plane. Here, the mass m is replaced by the energy E. (We shall put ħ = c = 1, E = (p2+m2)1/2 for a free particle of momentum p.) However, since the coupling to the electromagnetic field occurs by the replacement p → p + e A(t,r), the effective equation is not the best place for the introduction of the vector potential A. Besides, it may also be of interest to take a look at possible spin effects.
KeywordsDirac Equation Transverse Energy Transverse Motion Zeeman Effect Landau Gauge
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