In:
Journal of Mathematical Physics, AIP Publishing, Vol. 20, No. 6 ( 1979-06-01), p. 979-983
Abstract:
The following theorem is proved. Let D (ω) be an operator with eigenvalues and eigenfunctions {dk(ω), νk(ω) }, where ω is a complex parameter. Given a complex number dk0, let ω0 be such that dk(ω0) =〈Ṽk(ω0) ‖D (ω0) ‖νk(ω0) 〉=dk0, where Ṽk(ω0) is the dual eigenfunction to νk(ω0). Suppose ψ and Ṽ approximate νk(ω0) and Ṽk(ω0), respectively, to order ε. Then, if D (ω) is analytic in ω in the neighborhood of ω0, and if ω′ is such that 〈Ṽ‖D (ω′) ‖ψ〉=dk0, ω′ usually will approximate ω0 to order ε2. By applying this theorem it is shown that roots of the inhomogeneous plasma dispersion relation usually will be accurate to second order if the associated normal modes and their duals are known merely to first order. The theorem can also be applied to solutions of the dispersion relation in a truncated function space.
Type of Medium:
Online Resource
ISSN:
0022-2488
,
1089-7658
Language:
English
Publisher:
AIP Publishing
Publication Date:
1979
detail.hit.zdb_id:
1472481-9
