The quantum-mechanical movement of an electron in parallel magnetic and electric fields
DOI:
https://doi.org/10.15407/dopovidi2014.09.061Keywords:
electric fields, electron's movement, magnetic fieldsAbstract
The quantum mechanical problem of the electron movement in external electric and magnetic fields is considered. It is shown that this problem can be transformed to the solution of two independent differential equations describing the electron longitudinal and transverse movements. These solutions of the obtained differential equations are expressed with the special Hermite and Airy functions of order 1/3. This result is the theoretical approvement of Blatt's assumption on the independence of the penetrating coefficient through a potential barrier on the magnetic field by metal electron in the collinear electric and magnetic fields at the calculation of the field emission current density.
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