Correspondence between quantum mechanical and classical treatments of ion–electron collisions in a magnetic field
Abstract
The energy transfer of a heavy ion due to electron–ion collisions in a magnetic field is treated within perturbation theory both quantum mechanically and classically. For the quantum treatment the unperturbed Landau levels are represented either in a Cartesian or in a cylindrical basis. In both the cases the classical limit of the quantum mechanical expression is investigated and compared to the energy transfer in a fully classical treatment. It is demonstrated that the classical limit is more transparent in the cylindrical coordinates than in the Cartesian ones as the first case allows a connection to a classical description in terms of the impact parameter.
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