An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

Abstract

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean 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.

13 pages, 1 figure

References in corpus (3)

• Exceptional Points of Non-hermitian Operators
• PT-Symmetric Quantum Mechanics: A Precise and Consistent Formulation
• The Physical Interpretation of PT-invariant Potentials

Cited by in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Spectral singularities and Bragg scattering in complex crystals
• Detecting Broken PT-Symmetry
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra