Nodal theorems for the Dirac equation in d >= 1 dimensions

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A single particle obeys the Dirac equation in d ≥ 1 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 x≥ 0. The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases d=1 and d > 1, which specify the relationship between the numbers of nodes n₁ and n₂ in the upper and lower components of the Dirac spinor. For d=1, n₂ = n₁ + 1, whereas for d >1, n₂ = n₁ +1 if kd > 0, and n₂ = n₁ if kd < 0, where kd = τ(j + d-2/2), and τ= ± 1. This work generalizes the classic results of Rose and Newton in 1951 for the case d=3. Specific examples are presented with graphs, including Dirac spinor orbits (ψ₁(r), ψ₂(r)), r ≥ 0.