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Physical Review A

Generalized coherent states for electrons in external fields and application to potential scattering

Sándor Varró, F. Ehlotzky

Published Jul 1, 1987• 7 citations

Abstract

By continuing earlier investigations, generalized coherent states are introduced to describe the quasiclassical motion of electrons in a microwave and in a homogeneous magnetic field. The microwave is circularly polarized and propagates along the direction of the magnetic field. In view of possible applications to laboratory plasmas, the problem is treated nonrelativistically and the microwave is taken in the dipole approximation. The generalized coherent states emerge in polar coordinates (\ensuremath{\rho},\ensuremath{\varphi}) from ordinary Landau states \ensuremath{\Vert}l,m> by an appropriate choice of unitary and displacement operations. These coherent states are shown to form a complete and orthonormal set. Consequently, these states may be conveniently used for the description of scattering processes. As an example, scattering of electrons by a screened Coulomb potential is considered in the presence of the above two external fields. For simplicity, the scattering potential is treated in the first-order Born approximation. The quasiclassical features of the corresponding cross sections for the induced nonlinear processes are discussed.

DOI: 10.1103/physreva.36.497

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Scattering of light by an electron embedded simultaneously in a uniform magnetic field and in a microwave field is first analysed within the framework of classical electrodynamics. It is shown that the intensities of the different components of the scattered light can be increased by the presence of the magnetic field. Then coherent quantum states of the electron in the same field configuration are constructed and are applied to the description of the scattering process using semiclassical methods. The results of the classical and semiclassical calculations are compared and discussed and various limiting cases are considered to show the connection with previously published work.

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