1980/08/01 by Nimrod Moiseyev, Shmuel Friedland · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #Electromagnetic Scattering and Analysis
paper · doi:10.1103/physreva.22.618
openalex publication_date 1980/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The incomplete spectrum of finite complex-scaled Hamiltonian matrices H_\ensuremathη is studied. It is pointed out that the occurrence of an incomplete spectrum of complex-scaled Hamiltonians in the finite-element approximation is neither accidental nor rare, and the existence of a defective eigenvector (orthogonal to itself) of H_\ensuremathη can be associated with a complex-stationary point which represents the resonance state. A physical interpretation of the incomplete spectrum (the eigenvalues of a defective Hamiltonian matrix) is given, supported by numerical results for e^\ensuremath--He+ scattering worked out as an example. The numerical procedure suggested here for the purpose of identifying the resonance state with the eigenvalue associated with the defective eigenvector of H_\ensuremathη, may prove to be not very practical. This is so as long as only relatively small basis sets are used. However, in the finite-element approximation, this procedure does yield a better understanding of the behavior of the resonance solution.