2013/10/21 by Paolo Amore
Computer Science · Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Mathematical functions and polynomials #Matrix Theory and Algorithms #Mode (computer interface) #Order (exchange) #Spectral Theory in Mathematical Physics #Sum rule in quantum mechanics #Zero (linguistics) #Zero mode #math-ph #math.MP
paper · pdf · doi:10.1016/j.aop.2014.06.019
14 pages, one figure
arxiv created 2013/10/21 · openalex publication_date 2014/06/26 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that the formulas for the sum rules for the eigenvalues of inhomogeneous systems that we have obtained in two recent papers are incomplete when the system contains a zero mode. We prove that there are finite contributions of the zero mode to the sum rules and we explicitly calculate the expressions for the sum rules of order one and two. The previous results for systems that do not contain a zero mode are unaffected.