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Acta Physica Sinica

DOUBLE WAVE DESCRIPTION OF THE MOTION FOR A CHARGED PARTICLE IN MASS SPECTROMETER

HUANG XIANG-YOU, 北京大学物理系,北京100871

Published Jan 1, 1996• 1 citation
Publisher

Abstract

When and where a charged particle with given energy will enter or leave the magnetic field in a mass spectrometer, and how we use quantum mechanics to calculate them are interesting problems. The double-wave description of the system leads to the results that are similar to that of classical mechanics but the energies of particles take quantized discrete values.

DOI
10.7498/aps.45.729

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Brazilian Journal of Physics•Sep 1, 1999•7 citations
When and where a charged particle with given energy will enter or leave the magnetic field in a mass spectrometer, and how we use quantum mechanics to calculate them are interesting problems. The double-wave description of the system leads to the results that are similar to that of classical mechanics but the energies of particles take quantized discrete values.
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.
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.