Group-theoretical approach to Bloch electron in magnetic field problem

Group-theoretical approach to Bloch electron in magnetic field problem

In this paper magnetic-translation group theory is extended to include full rotational symmetry of Hamiltonian. Proper generalization of small representation and star of the representation concepts are derived. Irreducible representations of magnetic-translation group and magnetic-space group are pr...

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Veröffentlicht in:Journal of mathematical physics 2010-06, Vol.51 (6), p.062104-062104-15
1. Verfasser: COSIC, Marko
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic group theory
DIFFERENTIAL EQUATIONS
ELECTRONS
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUATIONS
Exact sciences and technology
FERMIONS
GROUP THEORY
HAMILTONIANS
IRREDUCIBLE REPRESENTATIONS
LEPTONS
MAGNETIC FIELDS
MATHEMATICAL METHODS AND COMPUTING
Mathematical methods in physics
MATHEMATICAL OPERATORS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
Physics
QUANTUM OPERATORS
Quantum physics
SCHROEDINGER EQUATION
Sciences and techniques of general use
SPACE GROUPS
SYMMETRY
SYMMETRY GROUPS
WAVE EQUATIONS
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Zusammenfassung:In this paper magnetic-translation group theory is extended to include full rotational symmetry of Hamiltonian. Proper generalization of small representation and star of the representation concepts are derived. Irreducible representations of magnetic-translation group and magnetic-space group are presented. Correct form of symmetrized basis function is derived, reflecting symmetry of the magnetic-point group. From viewpoint of group theory reduction of Hamiltonian symmetry group caused by magnetic field and splitting of energy levels is investigated.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3453601