Semiclassical quantisation rules for the Dirac and Pauli equations

Abstract

We derive explicit semiclassical quantisation conditions for the Dirac and Pauli equations. We show that the spin degree of freedom yields a contribution which is of the same order of magnitude as the Maslov correction in Einstein-Brillouin-Keller quantisation. In order to obtain this result a generalisation of the notion of integrability for a certain skew product flow of classical translational dynamics and classical spin precession has to be derived. Among the examples discussed is the relativistic Kepler problem with Thomas precession, whose treatment sheds some light on the amazing success of Sommerfeld's theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1--91].

36 pages, 2 figures

References in corpus (6)

• A semiclassical approach to the Dirac equation
• Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles
• Semiclassical limit of the Dirac equation and spin precession
• Semiclassical form factor for chaotic systems with spin 1/2
• Quantum and classical ergodicity of spinning particles
• Torus quantization for spinning particles

Cited by in corpus (18)

• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Bound states in inhomogeneous magnetic field in graphene: a semiclassical approach
• Spinoptics in a stationary spacetime
• Scattering of circularly polarized light by a rotating black hole
• Ultrafast dynamics of photoinduced charge separation
• Disarming the Ultimate Historical Challenge to Scientific Realism
• Dirac equations in curved space-time versus Papapetrou spinning particles
• Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula and applications to the graphene-type systems
• Electromagnetic Field Theory without Divergence Problems 2. A Least Invasively Quantized Theory
• Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
• Semiclassical quantization of spinning quasiparticles in ballistic Josephson junctions
• The fine structure of Weber's hydrogen atom -- Bohr-Sommerfeld approach
• On the Schrödinger spectrum of a hydrogen atom with electrostatic Bopp-Landé-Thomas-Podolsky interaction between electron and proton
• Semiclassical study of edge states and transverse electron focusing for strong spin-orbit coupling
• Semiclassical propagation of coherent states with spin-orbit interaction
• On general-relativistic hydrogen and hydrogenic ions
• Do particles and anti-particles really annihilate each other?
• Semiclassical perspective on Landau levels and Hall conductivity in an anisotropic Cubic Dirac Semi-Metal and the peculiar case of star-shaped classical orbits