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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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§1.18(v) Point Spectra and Eigenfunction Expansions

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§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). … ►

§1.18(viii) Mixed Spectra and Eigenfunction Expansions

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2: Bibliography D

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Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.

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ISSN 0021-9991, MathReview, ZentralBlatt

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§22.11.

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Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1837, pp. 45–81 (German).

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Notes:

Reprinted in G. Lejeune Dirichlet’s Werke, Band I, pp. 313–342, Reimer, Berlin, 1889 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.

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ISBN 0-8284-0225-6, Link, MathReview

Referenced by:

§25.15(i).

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Über die Bestimmung der mittleren Werthe in der Zahlentheorie. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1849, pp. 69–83 (German).

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Notes:

Reprinted in G. Lejeune Dirichlet’s Werke, Band II, pp. 49–66, Reimer, Berlin, 1897 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.

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ISBN 0-8284-0225-6, Link, MathReview

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§27.11.

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3: Charles W. Clark

… ► Nayfeh), published by Gordon and Breach in 1985, Atomic Spectra and Collisions in External Fields (with M. …

4: Bibliography M

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The supports of measures associated with orthogonal polynomials and the spectra of the related selfadjoint operators. Rocky Mountain J. Math. 21 (1), pp. 501–527.

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ISSN 0035-7596, Document, Link, MathReview (T. S. Chihara)

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§18.2(xi).

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Mathieusche Funktionen und Sphäroidfunktionen mit Anwendungen auf physikalische und technische Probleme. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXI, Springer-Verlag, Berlin (German).

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

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Table 28.1.1, §28.10(i), §28.11, §28.12(i), §28.12(ii), §28.12(iii), §28.14, §28.15(i), §28.15(ii), §28.16, §28.17, §28.19, §28.2(ii), §28.2(iii), §28.2(iv), §28.2(v), §28.2(vi), §28.20(ii), §28.20(iii), §28.20(vi), §28.20(vii), §28.22(i), §28.22(ii), §28.23, §28.24, §28.25, §28.28(i), 2nd item, 3rd item, §28.33(ii), item (e), item (d), §28.4(i), §28.4(ii), §28.4(iii), §28.4(iv), §28.4(v), §28.4(vi), §28.4(vi), §28.5(i), §28.5(i), §28.6(i), §28.6(ii), §28.7, §28.7, §28.8(i), §28.8(ii), §28.9, Ch.28, §30.1, §30.10, §30.11(iii), §30.11(iii), §30.11(iv), §30.11(v), §30.11(vi), §30.11(vi), §30.13(i), §30.13(ii), §30.13(iii), §30.13(iv), §30.13(v), §30.13(v), §30.14(i), §30.14(ii), §30.14(iii), §30.14(iv), §30.14(v), §30.14(v), §30.16(i), §30.16(i), §30.2(i), §30.2(ii), §30.3(i), §30.3(ii), §30.3(iii), §30.3(iv), §30.4(i), §30.4(ii), §30.4(iv), §30.5, §30.5, §30.6, §30.6, §30.8(i), §30.8(ii), §30.9(i), §30.9(i), §30.9(ii), §30.9(ii), Ch.30, Notations P, Notations P, Notations Q, Notations Q.

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5: 33.22 Particle Scattering and Atomic and Molecular Spectra

§33.22 Particle Scattering and Atomic and Molecular Spectra

… ►Positive-energy functions correspond to processes such as Rutherford scattering and Coulomb excitation of nuclei (Alder et al. (1956)), and atomic photo-ionization and electron-ion collisions (Bethe and Salpeter (1977)). … ►The negative-energy functions are widely used in the description of atomic and molecular spectra; see Bethe and Salpeter (1977), Seaton (1983), and Aymar et al. (1996). …

6: Bibliography N

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Die Gammafunktion. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten. Chelsea Publishing Co., New York (German).

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Notes:

Both books are textually unaltered except for correction of errata.

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MathReview

Referenced by:

N. Nielsen (1906a), N. Nielsen (1906b).

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7: Bibliography I

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Theta Functions. Springer-Verlag, New York.

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Notes:

Die Grundlehren der mathematischen Wissenschaften, Band 194

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ISBN 3540056998, MathReview (H. Klingen), ZentralBlatt

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§21.5(ii), §21.8, Ch.21.

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8: Bibliography H

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The combination of $R$-matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr. J. Phys. B 26 (12), pp. 1775–1790.

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ISSN 0953-4075, Document, MathReview

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4th item.

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9: Bibliography W

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Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Pure and Applied Physics. Vol. 5, Academic Press, New York.

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Notes:

Expanded and improved ed. Translated from the German by J. J. Griffin.

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ISBN 0-12-750550-4, MathReview (A. S. Wightman), ZentralBlatt

Referenced by:

§34.12.

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10: Bibliography S

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

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ISBN 0-471-78835-X

Referenced by:

§34.12.

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

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Notes:

A second printing with corrections was published in 1996.

Referenced by:

§34.12.

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