Numerical analysis of quantum-mechanical non-uniform E×B drift: Non-uniform electric field

Abstract

We have numerically solved the two-dimensional time-dependent Schrödinger equation for a charged particle in the presence of a non-uniform electric field E = E ≤(1- y / L_E ) e_y as well as a non-uniform magnetic field B = B ≤(1- y / L_B ) e_z. It is shown that such a non-uniformity of the electric field does not affect the time rate of the variance, or uncertainty, changes in position and momentum, while that of the magnetic field does.

Keywords

Schrödinger equation uncertainty non-uniform magnetic field non-uniform electric field quantum mechanical effect expansion rate GPU parallel computing

References

Oikawa

, Kosaka

and Chan

P.K.

, Plasma Fusion Res9 (2014), 3401033.

Oikawa

and Chan

P.K.

, Plasma Fusion Res8 (2013), 2401142.

Chan

P.K.

, Oikawa

and Okubo

, Plasma Fusion Res7 (2012), 2401034.

Oikawa

, Okubo

and Chan

P.K.

, Plasma Fusion Res7 (2012), 2401106.

Oikawa

, Shimazaki

and Okubo

, Plasma Fusion Res6 (2011), 2401058.

Natori

and Munehisa

, J Phys Soc Jpn66 (1997), 351-359.

Sakurai

J.J.

, Modern Quantum Mechanics, Rev. ed., (Addison-Wesley, Reading, 1994).

Landau

L.D.

and Lifshitz

E.M.

, Quantum Mechanics: Non-relativistic Theory, 3rd ed., translated from the Russian by J. B. Sykes and J. S. Bell (Pergamon Press, Oxford, 1977).

http://www.nvidia.com.

10.

Huba

J.D.

, ``NRL PLASMA FORMULARY'', Naval Research Laboratory, 2013.