[Table of Contents]

Plasma and Fusion Research

Volume 7, 2401034 (2012)

Regular Articles

Numerical Analysis of Quantum Mechanical ∇B Drift II
Poh Kam CHAN, Shun-ichi OIKAWA1) and Emi OKUBO
Graduate School of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan
Faculty of Engineering, Hokkaido University, N-13, W-8, Sapporo 060-8628, Japan
(Received 8 December 2011 / Accepted 2 March 2012 / Published 10 May 2012)


We have solved the two-dimensional time-dependent Schrödinger equation for a single particle in the presence of a non-uniform magnetic field for initial speed of 10-100m/s, mass of the particle at 1-10mp, where mp is the mass of a proton. Magnetic field at the origin of 5-10T, charge of 1-4 e, where e is the charge of the particle and gradient scale length of 2.610 × 10−5 -5.219m. It was numerically found that the variance, or the uncertainty, in position can be expressed as dσr2 /dt = 4.1 ħv0/qB0LB, where m is the mass of the particle, q is the charge, v0 is the initial speed of the corresponding classical particle, B0 is the magnetic field at the origin and LB is the gradient scale length of the magnetic field. In this expression, we found out that mass, m does not affect our newly developed expression.


grad-B drift, magnetic length, Landau state, quantum mechanical scattering, plasma, diffusion, expansion time, expansion rate of variance

DOI: 10.1585/pfr.7.2401034


  • [1] S. Oikawa, T. Shimazaki and E. Okubo, Plasma Fusion Res. 6, 2401058 (2011).
  • [2] http://www.nvidia.com
  • [3] L.D. Landau and E.M. Lifshitz, Quantum Mechanics: Nonrelativistic Theory, 3rd ed., translated from the Russian by J.B. Sykes and J.S. Bell (Pergamon Press, Oxford, 1977).

This paper may be cited as follows:

Poh Kam CHAN, Shun-ichi OIKAWA and Emi OKUBO, Plasma Fusion Res. 7, 2401034 (2012).