Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 39, Issue 1, Pages 235-245Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/39/1/017
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A non-Hermitian operator does not necessarily have a complete set of eigenstates, contrary to a Hermitian one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.
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