Conjecture on the analyticity of -symmetric potentials and the reality of their spectra
Conjecture on the analyticity of -symmetric potentials and the reality of their spectra
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DOI：
10.1088/1751-8113/41/39/392005
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发表时间：
2008-07
期刊：
影响因子：
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通讯作者：
C. Bender;Daniel W. Hook;L. Mead
中科院分区：
文献类型：
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作者：
C. Bender;Daniel W. Hook;L. Mead
如果势V(X)→∞为x→±∞，则厄米哈密顿量H=p2+V(X)的谱是实的离散的。然而，如果V(X)是复数和对称的，则可以猜想，除非在极少数特殊情况下，V(X)必须是解析的，才能有实谱。这个猜想是用位势V(X)=(Ix)a|x|b来证明的，其中a，b是实数。
The spectrum of the Hermitian Hamiltonian H = p2 + V(x) is real and discrete if the potential V(x) → ∞ as x → ±∞. However, if V(x) is complex and -symmetric, it is conjectured that, except in rare special cases, V(x) must be analytic in order to have a real spectrum. This conjecture is demonstrated by using the potential V(x) = (ix)a|x|b, where a, b are real.