Abstract
The problem of quantum motion of a charged particle in a magnetic field is considered in the framework of the tomographic probability representation. The coherent and Fock states of a charge moving in a time-dependent homogeneous magnetic field are studied in the tomographic probability representation. These states are expressed in terms of the quantum tomograms. The Fock state tomograms are given in the form of probability distributions described by multivariable Hermite polynomials with time-dependent arguments. These results are then generalized and applied to calculate the transition probabilities between the Landau levels for the case of transitions between stationary states of different magnetic fields, when the initially constant field becomes time dependent and then stays at some constant value again. The problem is studied in terms of wave functions and symplectic tomograms as well.
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