Exact sum rules for inhomogeneous strings

Journal Article · Fri Nov 15 04:00:00 EST 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.05.011· OSTI ID:22224242

Amore, Paolo

We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order N may be obtained in terms of a diagrammatic expansion, with (N−1)!/2 independent diagrams. These sum rules are used to derive upper and lower bounds to the energy of the fundamental mode of an inhomogeneous string; we also show that it is possible to improve these approximations taking into account the asymptotic behavior of the spectrum and applying the Shanks transformation to the sequence of approximations obtained to the different orders. We discuss three applications of these results. -- Highlights: •We derive an explicit expression for the sum rules of an inhomogeneous string. •We obtain a diagrammatic representation for the sum rules of a given order. •We obtain precise bounds on the lowest eigenvalue of the string.

• OSTI ID: 22224242
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 338; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
BOUNDARY CONDITIONS
DENSITY
DIAGRAMS
EIGENVALUES
PERTURBATION THEORY
SPECTRA
SUM RULES
TRANSFORMATIONS