https://doi.org/10.1140/epjp/s13360-020-00820-y
Regular Article
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
Received:
23
February
2020
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.
I would like to dedicate this paper to the memory of my beloved father Carmine De Vincenzo Di Fresca, who passed away unexpectedly on March 16, 2018. That day something inside of me also died.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
