Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant.

Authors: Thylwe, K.-E., McCabe, P.
Document Type: Article
Pubstate: Accepted
Journal: Journal of Mathematical Physics
Volume: 54   052301
Year: 2013


It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov- type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.