By Carl Bender and others

The spectrum of the Hermitian Hamiltonian *H=p^2+V(x)* is real and discrete if the potential *V(x)\to\infty* as *x\to\pm\infty*. However, if *V(x)* is complex and PT-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... Show more

July 3, 2008

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Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra

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