continuous spectra

SearchAdvancedHelp

(0.002 seconds)

3 matching pages

1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►

§1.18(vi) Continuous Spectra and Eigenfunction Expansions: Simple Cases

… ►

§1.18(vii) Continuous Spectra: More General Cases

►More generally, continuous spectra may occur in sets of disjoint finite intervals $[{\lambda }_a,{\lambda }_b]\in (0,\mathrm{\infty })$, often called bands, when $q(x)$ is periodic, see Ashcroft and Mermin (1976, Ch 8) and Kittel (1996, Ch 7). … …

2: 18.39 Applications in the Physical Sciences

… ►The properties of $V(x)$ determine whether the spectrum, this being the set of eigenvalues of $\mathscr{H}$, is discrete, continuous, or mixed, see §1.18. … ►Such a superposition yields continuous time evolution of the probability density ${|\mathrm{\Psi }(x,t)|}^2$. … ►Brief mention of non-unit normalized solutions in the case of mixed spectra appear, but as these solutions are not OP’s details appear elsewhere, as referenced. … ►An important, and perhaps unexpected, feature of the EOP’s is now pointed out by noting that for 1D Schrödinger operators, or equivalent Sturm-Liouville ODEs, having discrete spectra with $L^2$ eigenfunctions vanishing at the end points, in this case $\pm \mathrm{\infty }$ see Simon (2005c, Theorem 3.3, p. 35), such eigenfunctions satisfy the Sturm oscillation theorem. … ►Namely for fixed $l$ the infinite set labeled by $p$ describe only the $L^2$ bound states for that single $l$, omitting the continuum briefly mentioned below, and which is the subject of Chapter 33, and so an unusual example of the mixed spectra of §1.18(viii). …

3: Bibliography S

… ►

Principles of Atomic Spectra. John Wiley & Sons Ltd., New York.

ⓘ

External Links:

ISBN 0-471-78835-X

Referenced by:

§34.12.

Encodings:

BibTeX

… ►

Operators with Singular Continuous Spectrum: I. General Operators. Annals of Mathematics 141 (1), pp. 131–145.

ⓘ

External Links:

MathReview Entry

Referenced by:

§1.18(vii).

Encodings:

BibTeX

… ►

Atomic Spectra and Radiative Transitions. 2nd edition, Springer-Verlag, Berlin.

ⓘ

Notes:

A second printing with corrections was published in 1996.

Referenced by:

§34.12.

Encodings:

BibTeX

…