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Journal of Beijing Union University

Quantum Effect of the Motion of Charge in Magnetic Field

Zhao Min

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

In Newtonian mechanics,the motion of the charge in magnetic field is in equidistance helical line.It is composed of the uniform motion in magnetic field and the circular motion vertical to the magnetic field.In quantum mechanics,its motion is two-dimensional resonance.Its energy level is separate.Its wave function is probability.With this theory to explain magnetic focusing a large number of charge moving in the magnetic field are not at a point 100%.Instead,they wwill be dispersed according to probability.

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In Newtonian mechanics,the motion of the charge in magnetic field is in equidistance helical line.It is composed of the uniform motion in magnetic field and the circular motion vertical to the magnetic field.In quantum mechanics,its motion is two-dimensional resonance.Its energy level is separate.Its wave function is probability.With this theory to explain magnetic focusing a large number of charge moving in the magnetic field are not at a point 100%.Instead,they wwill be dispersed according to probability.
In Newtonian mechanics, the motion of the charge in the magnetic field is the equidistance helical line. It is composed of the uniform motion in magnetic field’s direction and the circular motion in vertical direction. In quantum mechanics, its motion is the two-dimensional resonance. Its energy level is separate. Its wave function is probability. With this theory, magnetic focusing is explained to that a large number of charge moving in the magnetic field is not 100% at a point. They will be dispersed according to probability.
The motion of a particle with charge q and mass m in a magnetic field given by B = kB0 + B1 [icos(omegat) + jsin(omegat)] and an electric field which obeys Ñ ×E = - ¶ B/ ¶ t is analysed classically and quantum-mechanically. The use of a rotating coordinate system allows the analytical derivation of the particle classical trajectory and its laboratory wavefunction. The motion exhibits two resonances, one at omega = omegac = -qBo/m, the cyclotron frequency, and the other at omega = omegaL = -qBo/2m, the Larmor frequency. For omega at the first resonance frequency, the particle acquires a simple closed trajectory, and the effective hamiltonian can be interpreted as that of a particle in a static magnetic field. In the second case a term corresponding to an effective static electric field remains, and the particle orbit is an open line. The particle wave function and eigenenergies are calculated.
Double wave quantum theory is applied to describe the motion of charged particle in a uniform magnetic field. This description of the motion of the particle is complete. One can tell the value of an arbitrary physical quantity at any time. The probability and the formula to calculate mean values in ordinary quantum mechanics comes from the average of double wave description over a certain ensemble. The rule of gauge transformation in quantum mechanics can be seen from the average over an ensemble.