ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
It is supposed that a single fermion with Hamiltonian H=α⋅p+βμ(r)+φ(r), where μ(r) and φ(r) are central potentials, obeys the Dirac equation. If ψ1(r) and ψ2(r) are the radial factors in the Dirac spinor, then the graph {ψ1(r), ψ2(r)} for r∈(0,∞) is called a spinor orbit. In cases where discrete eigenvalues exist, the corresponding spinor orbit eventually returns to the origin. However, if there is a constant a≥0 such that, for r〉a, the three functions φ(r), φ(r)/μ(r), and rμ(r) increase monotonically without bound, then it is proved that the spinor orbit must eventually be confined to an annular region excluding the origin. Consequently, the spinor orbit approaches a "spinor circle,'' the spinor is not L2, and there are no eigenvalues. This happens, for example, if μ is constant and φ(r) is any monotone increasing and unbounded potential. In such cases the radius of the spinor circle is sensitive to the energy, and instead of eigenvalues one finds a sequence of resonant energies for which the radii of the spinor circles are local minima.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527626
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