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Richard L. Hall and Petr Zorin Nodal theorems for the Dirac equation in d ≥ 1 dimensions Annalen der Physik 526

Article first published online: 1 OCT 2013 | DOI: 10.1002/andp.201300161

A single particle obeys the Dirac equation in inline image 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 inline image The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases inline image and inline image, which specify the relationship between the numbers of nodes n1 and n2 in the upper and lower components of the Dirac spinor. For inline image, inline image whereas for inline image inline image if inline image and inline image if inline image where inline image and inline image This work generalizes the classic results of Rose and Newton in 1951 for the case inline image Specific examples are presented with graphs, including Dirac spinor orbits inline image

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