The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Quantum Electrodynamics in Strong Magnetic Fields. I. Electron States
Open accessAbstract
Dirac's equation in the presence of a static magnetic field is solved in terms of both cartesian and cylindrical coordinates, and solutions are found for three different spin operators. Choosing the spin to correspond to the parallel component Ilz of the magnetic moment operator leads to wavefunctions (a) which are symmetric between electron and positron states and (b) which are eigenfunctions of the Hamiltonian including radiative corrections. A vertex function [y:',~(k)l~ is defined and shown to be proportional to a gauge independent quantity [T::~(k)l". Symmetry properties of [T~:~(k)l~ are derived in the case where the spin corresponds to Ilz. The use of the vertex function is illustrated by deriving the electron propagator in coordinate space from the vacuum expectation value. Properties of functions J~, _n(x) which appear extensively and are related to generalized Laguerre polynomials are derived and summarized in the Appendix.
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“Both for the Pauli and the Dirac equations, the spatial dependence of the wave-function in Cartesian coordinates can be expressed as a Hermite polynomial times a Gaussian function (Melrose and Parle 1983) only the energy eigenvalues for the Landau quantized states are different.”
From Quantum kinetic theory of plasmas (2022) · cites this paper as Melrose and Parle 1983
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Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
Tables of Integrals, Series, and Products.
Bello, A. D., Gradshteyn, I. S., RYZHIK, I. M., & Jeffrey, A. (1995) · Journal of the Royal Statistical Society Series D (The Statistician) · doi:10.2307/2348458 · Cited by 5,860
Sokolov, A. A., & Ternov, I. M. (1967) · Russian Physics Journal · doi:10.1007/bf00820300 · Cited by 228
Research works printed but not linked: 4
- Berestetskii, V. B., Lifshitz, E. M., and Pitaevskii, L. P. (1971). 'Relativistic Quantum Theory, Part I' (Pergamon: Oxford).
- Itzykson, c., and Zuber, J.-B. (1980). 'Quantum Field Theory' (McGraw-Hili: New York).
- Kallen, A. O. G. (1958). In 'Handbuch der Physik', Vol. 5 (Ed.A . S. Flugge), Part 1 (Springer: Berlin).
- Melrose, D. B., and Parle, A. J. (1981). Proc. Astron. Soc. Aust. 4, 214.
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Quantum kinetic theory of plasmas
Brodin, G., & Zamanian, J. (2022) · Reviews of Modern Plasma Physics · doi:10.1007/s41614-022-00065-5 · Cited by 37
Metadata
- Authors
- Melrose, D., & Parle, A.
- Affiliations
- The University of Sydney (AU)
- Venue
- Australian Journal of Physics
- Publisher
- CSIRO Publishing
- Published
- 1983-12-01
- Volume
- 36
- Issue
- 6
- Pages
- 755-774
- ISSN
- 0004-9506 (ISSN-L)
- 1446-5582
- OpenAlex
- W2051875410
- Cited by
- 76
- References
- 3
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 2 · 2023: 1 · 2022: 1 · 2020: 2 · 2019: 5 · 2018: 2 · 2017: 7 · 2016: 3 · 2015: 2 · 2014: 4 · 2013: 1 · 2012: 1
- FWCI
- 0.55
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Australian Journal of Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Molecular Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- quantum electrodynamics, high magnetic fields, Dirac equation, electronic states, positron states, spin operators, radiative corrections, vertex functions, gauge independence, electron propagator, coordinate space, vacuum expectation value, generalized Laguerre polynomials
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