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Starting from Heisenberg's point of view, a semi-classical quantization method is introduced for 2D Bloch electrons in a magnetic field. The underlying lattice structure is used to define an algebraic structure. The (rotation) algebra so defined is non commutative, but allows for a systematic expansion of the magnetic energy levels, free energy, etc. near zero as well as an arbitrary rational flux. All previously derived results are recovered as special cases, but without involving wave function considerations (WKB, equation-of-motion methods, etc.). New results, up to second order in the magnetic flux, are explicitly derived and simple examples are used to illustrate our general algebraic formalism.
Rammal et al. (Mon,) studied this question.