On 3D and 1D Weyl particles in a 1D box
Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, A.P. 47145, 1041-A, Caracas, Venezuela
Accepted: 29 September 2020
Published online: 10 October 2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020