Exploiting the property [ H ^ ^ , L ^ ^ z ] = 0 we chose eigenfunctions which diagonalize H ^ ^ and L ^ ^ z , The eigenvalue of L ^ ^ z is denoted by − − m z ℏ ℏ , where it is clear that m z ≥ ≥ − − n in the n th Landau level. However, it may be arbitrarily large, which is necessary to obtain the infinite degeneracy (or finite degeneracy per unit area) exhibited by the system.