PT-Symmetry, Canonical Decomposition, Perturbation Theory |
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Authors: | Emanuela Caliceti |
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Institution: | (1) Dipartimento di Matematica, Università di Bologna, 40127 Bologna, Italy |
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Abstract: | Let H be any PT-symmetric Schrödinger operator of the type H=-
2
+x
2
+igW(x), where W is a real polynomial, odd under reflection of all coordinates, gR, acting on L
2
(
R
d
). The proof is outlined of the following statements: PH is self-adjoint and its eigenvalues coincide with the eigenvalues of (H*H). Moreover the eigenvalues of (H*H), known as the singular values of H, can be computed via perturbation theory by Borel summability. |
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Keywords: | PT-symmetry singular values perturbation theory |
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