## ar X iv : 0 90 7 . 32 80 v 1 [ m at h - ph ] 1 9 Ju l 2 00 9 ON J - SELF - ADJOINT EXTENSIONS OF THE PHILLIPS SYMMETRIC OPERATOR

- S. KUZHEL, O. SHAPOVALOVA, L. VAVRYKOVYCH

Although the quantum bound-state energies may be generated by the so called PT −symmetric Hamiltonians H = PH†P 6 = H where P is, typically, parity, the spectrum only remains real and observable (i.e., in the language of physics, the PT −symmetry remains unbroken) inside a domain D of couplings. We show that the boundary ∂D (i.e., certain stability and… (More)

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