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Real spectra in non-Hermitian Hamiltonians having $$\mathcal{PT}$$ symmetry. (English) Zbl 0947.81018
Summary: The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition $$\mathcal P\mathcal T$$ of symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These $$\mathcal P\mathcal T$$ symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.

##### MSC:
 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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