THE WAVEFUNCTION OF THE ELECTRON IN A HOMOGENEOUS MAGNETIC-FIELD AND THE PLANE-WAVE STATE - ADIABATIC AND SUDDEN APPROXIMATIONS

摘要: Expansions of a plane wave in Landau states are derived corresponding to an adiabatic and sudden switching on the magnetic field. Two earlier solutions given by Faisal (1982) Ohsaki (1983) found be valid alternative expansions case, which differ only choice normalisations basis used. A result identical Ohsaki's is reobtained, since confined conservation energy large but finite area LxLy approximately 1/ gamma , perpendicular This requires sum over degenerate restricted within range. The upper lower limits this range derived. completeness relation Faisal's expansion shows that it also effectively automatically same states. In limit 0 both sets coefficients become results go desired plane-wave state. when field switches instantaneously from zero value, no longer consists fixed energy, new. two correspond different limiting cases any experimental situation, shown invalid at highest laboratory ( 20 kG) current use. situations discussed.