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SOLVED:As shown in Problem 5.14, the symmetry group for a finite 1D periodic lattice having cyclic boundary conditions with N periods between boundaries is the cyclic group of order N, with irreps of the form Γ^(p)=e^2 πi p / N(p=1,2,3, …, N) . Show that if the total length of the finite 1D lattice is L=a N, wavefunctions defined on the lattice obey (x+a)=e^i k a (x), or equivalently (x)=uk(x), where uk(x) is periodic, uk(x)=uk(x+a), and k ≡2 πp / L is called the crystal momentum. This result is
SOLVED:As shown in Problem 5.14, the symmetry group for a finite 1…
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