ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
With the aid of a method similar to the one we used in an earlier work (part I) a new Schrödinger-type field equation with logarithmic nonlinearity can be derived from a Fokker-Planck equation for a distribution function. This nonlinear field equation describes the frictinally damped motion of a system under the influence of a magnetic field and can be interpreted in the same way as the nonlinear Schrödinger-type equation (NLSE) derived in part I, where no magnetic fields were taken into account. The NLSE for the two-dimensional motion of a charged material system in a homogeneous magnetic field is solved exactly. The solutions are compared with the quantum-mechanical solutions of the corresponding undamped problem. The method is extended to include also anisotropic conditions; i.e., in the Fokker-Plank equation the diffusion constant has to be replaced by a diffusion matrix, as different diffusion constants may be possible for different space directions. We regard the three-dimensional motion under the combined influence of magnetic and electric fields according to K = (q/c)(v × B) + qE - mγv with Ey = (m/q)ωt2y, Ez = -(m/q)ωt2z, B = (0, 0, B) as an example. This is an approximation of the conditions existing in an ion cyclotron resonance spectrometry cell, neglecting an additional drift motion in the x direction which could be taken into account by Galilean transformation and gauge transformation. The corresponding NLSE for the coupled three-dimensional motion is specified and solved exactly.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560250210
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