We use an algebraic approach to the calculation of Landau levels for a uniform magnetic field in the symmetric gauge with a vector potential A→=12(B→xr→), where B→ is assumed to be constant. The magnetron quantum number constitutes the degeneracy index. An overall complex phase of the wave function, given in terms of Laguerre polynomials, is a consequence of the algebraic structure. The relativistic generalization of the treatment leads to fully relativistic bispinor Landau levels in the symmetric gauge, in a representation which writes the relativistic states in terms of their nonrelativistic limit, and an algebraically accessible lower bispinor component. Negative-energy states and the massless limit are discussed. The relativistic states can be used for a number of applications, including the calculation of higher-order quantum electrodynamic binding corrections to the energies of quantum cyclotron levels.



Publication Status

Open Access


National Science Foundation, Grant PHY–2110294

International Standard Serial Number (ISSN)

2470-0029; 2470-0010

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2023 American Physical Society, All rights reserved.

Publication Date

01 Jul 2023

Included in

Physics Commons