Exact sum rules for inhomogeneous systems containing a zero mode

Journal Article · Wed Oct 15 00:00:00 EDT 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.06.019· OSTI ID:22403412

Amore, Paolo

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. - Highlights: • We discuss the sum rules of the eigenvalues of inhomogeneous systems containing a zero mode. • We derive the explicit expressions for sum rules of order one and two. • We perform accurate numerical tests of these results for three examples.

• OSTI ID: 22403412
• Journal Information: Annals of Physics (New York), Vol. 349; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVALUES
NUMERICAL ANALYSIS
SUM RULES