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- W2115144393 abstract "Given a non-Hermitian matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note explains how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upon discretizing the configuration space, the system is described by a matrix of dimension three which turns out not to be diagonalizable for a critical strength of the interaction. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two." @default.
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- W2115144393 date "2005-09-01" @default.
- W2115144393 modified "2023-10-18" @default.
- W2115144393 title "How to test for diagonalizability: the discretized PT-invariant square-well potential" @default.
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- W2115144393 doi "https://doi.org/10.1007/s10582-005-0126-7" @default.
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