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It is shown that the PT symmetric Hamiltonian with the periodic potential V(x)=4cos2x+4iV0sin2x can be mapped into a Hermitian Hamiltonian for V0<0.5, by a similarity transformation. It is also shown that there exist a second critical point of the potential V(x), apart from the known critical point V0=0.5, for V0c∼0.888437 after which no part of the eigenvalues and the band structure remains real...
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