About the Project

discrete spectrum

AdvancedHelp

(0.001 seconds)

3 matching pages

1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
► The analogous orthonormality is … ►The point, or discrete spectrum of T is then given by 𝝈 p = { λ 0 , λ 1 , } . … ►►
Example 1: In one and two dimensions any q ⁢ ( x ) with a ‘Dip, or Well’ has a partly discrete spectrum
►The bound states are in the negative energy discrete spectrum, and the scattering states are in the positive energy continuous spectrum, 𝝈 c = [ 0 , ) , or, said more simply, in the continuum. …
2: 18.39 Applications in the Physical Sciences
►While non-normalizable continuum, or scattering, states are mentioned, with appropriate references in what follows, focus is on the L 2 eigenfunctions corresponding to the point, or discrete, spectrum, and representing bound rather than scattering states, these former being expressed in terms of OP’s or EOP’s. … ►However, in the remainder of this section will will assume that the spectrum is discrete, and that the eigenfunctions of ℋ form a discrete, normed, and complete basis for a Hilbert space. … ►Here are three examples of solutions for (18.39.8) for explicit choices of V ⁢ ( x ) and with the ψ n ⁢ ( x ) corresponding to the discrete spectrum. … ►The spectrum is entirely discrete as in §1.18(v). … ►The spectrum is entirely discrete as in §1.18(v). …
3: Bibliography F
►
  • M. V. Fedoryuk (1991) Asymptotics of the spectrum of the Heun equation and of Heun functions. Izv. Akad. Nauk SSSR Ser. Mat. 55 (3), pp. 631–646 (Russian).
  • ►
  • P. Flajolet and A. Odlyzko (1990) Singularity analysis of generating functions. SIAM J. Discrete Math. 3 (2), pp. 216–240.
  • ►
  • H. Flaschka and A. C. Newell (1980) Monodromy- and spectrum-preserving deformations. I. Comm. Math. Phys. 76 (1), pp. 65–116.
  • ►
  • A. S. Fokas, B. Grammaticos, and A. Ramani (1993) From continuous to discrete Painlevé equations. J. Math. Anal. Appl. 180 (2), pp. 342–360.
  • ►
  • A. S. Fokas, A. R. Its, and A. V. Kitaev (1991) Discrete Painlevé equations and their appearance in quantum gravity. Comm. Math. Phys. 142 (2), pp. 313–344.