A note on the invariant periodic potential

It is shown that the [inline image][inline image] symmetric Hamiltonian with the periodic potential [inline image][inline image] can be mapped into a Hermitian Hamiltonian for V sub(00.5, 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) sub(0)=0.5, for [inline image][inline image] after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.