On 3D and 1D Weyl particles in a 1D box
- URL: http://arxiv.org/abs/2007.06423v2
- Date: Mon, 12 Oct 2020 14:12:57 GMT
- Title: On 3D and 1D Weyl particles in a 1D box
- Authors: Salvatore De Vincenzo
- Abstract summary: We construct the most general families of self-adjoint boundary conditions for three (equivalent) Weyl Hamiltonian operators.
We also obtain and discuss throughout the article distinct results related to the Weyl equations in (3+1) and (1+1) dimensions.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We construct the most general families of self-adjoint boundary conditions
for three (equivalent) Weyl Hamiltonian operators, each describing a
three-dimensional Weyl particle in a one-dimensional box situated along a
Cartesian axis. These results are essentially obtained by using the most
general family of self-adjoint boundary conditions for a Dirac Hamiltonian
operator that describes a one-dimensional Dirac particle in a box, in the Weyl
representation, and by applying simple changes of representation to this
operator. Likewise, we present the most general family of self-adjoint boundary
conditions for a Weyl Hamiltonian operator that describes a one-dimensional
Weyl particle in a one-dimensional box. We also obtain and discuss throughout
the article distinct results related to the Weyl equations in (3+1) and (1+1)
dimensions, in addition to their respective wave functions, and present certain
key results related to representations for the Dirac equation in (1+1)
dimensions.
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