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.

• Received 27 December 2013

DOI:https://doi.org/10.1103/PhysRevA.92.032120