关于PT不变周期势V（x）= 4cos^2x +4iV_0sin2x的注记
A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
摘要：
证明了具有周期势V（x）= 4cos^2x +4iV_0sin2x的PT对称哈密顿量可以通过相似变换映射为$V_0<0.5$的厄米哈密顿量.对于$V_0^c ~ .888437$，除了已知的临界点$V_0=0.5$外，还存在势V（x）的第二个临界点，在该临界点之后，所有的本征值和能带结构都不为实.指出了这一发现的有关物理后果。
英文摘要：
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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