A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x

Details A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x

2010-04-19

arxiv.org/abs/1004.3218v1

Phys.Lett.A374:2605-2607,2010

Physics

Quantum Physics

Scientific paper

10.1016/j.physleta.2010.04.046

It is shown that the PT symmetric Hamiltonian with the periodic potential V(x) = 4 cos^2 x + 4 i V_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 $V_0^c ~ .888437$ after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.

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