Nodal theorems for the Dirac equation in d ≥ 1 dimensions |
| |
Authors: | Richard L. Hall Petr Zorin |
| |
Affiliation: | Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada, H3G 1M8 |
| |
Abstract: | A single particle obeys the Dirac equation in spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and monotone for The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases and , which specify the relationship between the numbers of nodes n1 and n2 in the upper and lower components of the Dirac spinor. For , whereas for if and if where and This work generalizes the classic results of Rose and Newton in 1951 for the case Specific examples are presented with graphs, including Dirac spinor orbits |
| |
Keywords: | Dirac equation nodal theorems Dirac spinor orbits |
|
|