Uncertainty Heisenberg principle of graphene and intersubband transitions of bulk GaN

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In the framework of the effective mass theory the Schrödinger equation is solved for the valence bands with $3\times3$ block Hamiltonian which are shown to be related with the symmetry group of C_{6v}. The exact solutions of the Schrödinger equations for materials with wurtzite band dispersion as well as uncertainty Heisenberg principle of graphene are found. For the honeycomb lattice of graphene with two carbon atoms per unit cell the Effective Hamiltonian of graphene based C_{3h}^{1} space symmetry group was found. Derivation of expressions of momentum matrix elements of intersubband transitions for bulk GaN are considered. In the article for the uncertainty Heisenberg principle for Dirac cone band dispersion the expression $\delta\textbf{p}=\sqrt{\overline{(\textbf{p}-\overline{\textbf{p}})^{2}}}=\fra c{\sqrt{5}+\iota\sqrt{3}}{2\sqrt{2}}$ has been found.

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