Confinement limit of a Dirac particle in two and three dimensions

Jian-Yuan Cheng

Unanyan, Otterbach, and Fleischhauer [Phys. Rev. A 79, 044101 (2009)] found that the confinement limit of a one-dimensional Dirac particle can be derived from the Dirac equation. The generalization of this problem to three dimensions is discussed in this paper. It shows that the three-dimensional Dirac particle in vector and scalar potentials has a confinement limit proportional to the modulus of expectation value of spin. This result obtained in Dirac equation is applicable for any Dirac particle confined in a finite region of space, even when vector and scalar potentials of quite general character are present. In addition, a Dirac particle confined in Lorentz scalar potential is discussed.

Mehmet Şimşek

Bernd Thaller, Sigrid Thaller

Jian-Yuan Cheng

Unanyan, Otterbach, and Fleischhauer [Phys. Rev. A 79, 044101 (2009)] found that the confinement limit of a one-dimensional Dirac particle in a symmetric potential is half its corresponding Compton length and can be derived from the Dirac equation. Then, Toyama and Nogami [Phys. Rev. A 81, 044106 (2010)] conjectured that a more stringent limit holds for any symmetric potential. I would like to show, in this Brief Report, that the confinement limit conjectured by Toyama and Nogami can be derived from the Dirac equation.

I. A. Howard, Norman Henry March

In early work, Lawes and March obtained a differential equation for an arbitrary number of independent harmonically confined fermions in one dimension, and very recently this result has been generalized to apply to three-dimensional (3D) isotropic harmonic confinement. Here, an exact solution of this 3D equation for the fermion particle density ρ( r ) is constructed, and the near-diagonal form of the Dirac density matrix is also obtained.

Garnet N. Ord, D. G. C. McKeon