# A note on the PT-invariant periodic potential Vx=4 cos^2 x 4 i V 0 sin 2x - Quantum Physics

A note on the PT-invariant periodic potential Vx=4 cos^2 x 4 i V 0 sin 2x - Quantum Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: It is shown that the PT symmetric Hamiltonian with the periodic potentialVx = 4 cos^2 x + 4 i V 0 sin 2x can be mapped into a Hermitian Hamiltonianfor $V 0<0.5$, by a similarity transformation. It is also shown that thereexist a second critical point of the potential Vx, apart from the knowncritical point $V 0=0.5$, for $V 0^c ~ .888437$ after which no part of theeigenvalues and the band structure remains real. Relevant physical consequenceof this finding has been pointed out.

Author: ** Bikashkali Midya, Barnana Roy, Rajkumar Roychoudhury**

Source: https://arxiv.org/