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PT-symmetric square well. (English) Zbl 0969.81521

Summary: Below a (comparatively large) measure of non-hermiticity Z=Z\(_0^{(crit)}>\)0 of a PT symmetrically complexified square well, bound states are constructed non-numerically. All their energies prove real and continuous in the (Hermitian) limit Z\(\rightarrow{}\)0. Beyond the threshold Z\(_0^{(crit)}\) (and, in general, beyond Z\(_m^{(crit)}\) at m=0,1,\(\cdots{}\)) the lowest two real energies (i.e., E\(_{2m}\) and E\(_{2m+1}\)) are shown to merge and disappear.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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