Use of Quantum Mechanical Methods to Obtain a Bohm-Type Coefficient of Diffusion

A Bohm-type coefficient of diffusion is obtained by means of a procedure starting from the Hamiltonian of a single electron in a dilute plasma in the presence of an external, uniform magnetic field of constant magnitude and an electrical potential that serves to simulate an electrical fluctuation which drives the guiding center drift. Using the concept of the differentiation of operators with respect to time, the formula for the well-known E × B drift velocity is recovered. Finally, the solution of a quantum mechanical equation of motion for the guiding center is found in the quasi-classical approximation to obtain a diffusion coefficient.