A note on the PT invariant periodic potential V(x)=4 cos2x+4iV0 sin 2x

It is shown that the PT symmetric Hamiltonian with the periodic potential V(x)= 4 cos(2)x + 4iV(0) sin 2x can be mapped into a Hermitian Hamiltonian for V-0 < 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 V-0 =0.5, for V-0(c) similar to 0.888437 after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out. (C) 2010 Elsevier B.V. All rights reserved.