A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
Quantum Physics
2011-01-04 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
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 , 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 , for after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.
Keywords
Cite
@article{arxiv.1004.3218,
title = {A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x},
author = {Bikashkali Midya and Barnana Roy and Rajkumar Roychoudhury},
journal= {arXiv preprint arXiv:1004.3218},
year = {2011}
}