wave functions

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31—40 of 77 matching pages

31: Bibliography V

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A. L. Van Buren, R. V. Baier, S. Hanish, and B. J. King (1972) Calculation of spheroidal wave functions. J. Acoust. Soc. Amer. 51, pp. 414–416.

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External Links:: Document, ZentralBlatt
Referenced by:: §30.16(ii), §30.18(iii).
Encodings:: BibTeX

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A. L. Van Buren, B. J. King, R. V. Baier, and S. Hanish (1975) Tables of Angular Spheroidal Wave Functions, Vol. 1, Prolate,

m=0

; Vol. 2, Oblate, m=0. Naval Res. Lab. Reports, Washington, D.C..

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Referenced by:: 5th item.
Encodings:: BibTeX

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Van Buren (website) Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation

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External Links:: Home Page
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, A. L. Van Buren and J. E. Boisvert (2002), A. L. Van Buren and J. E. Boisvert (2004), A. L. Van Buren and J. E. Boisvert (2007).
Encodings:: BibTeX

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32: 30.13 Wave Equation in Prolate Spheroidal Coordinates

§30.13 Wave Equation in Prolate Spheroidal Coordinates

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30.13.13

w_{2}(\eta)=a_{2}\mathsf{Ps}^{m}_{n}\left(\eta,\gamma^{2}\right)+b_{2}\mathsf{% Qs}^{m}_{n}\left(\eta,\gamma^{2}\right).

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, $\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the second kind, $m$ : nonnegative integer, $n\geq m$ : integer degree, $b_{j}$ : coefficients, $\eta$ : prolate spheroidal coordinate, $w_{j}$ : solution to DE, $\gamma^{2}=\kappa^{2}c^{2}$ : parameter and $a_{j}$ : coefficients
Referenced by:: §30.13(v), §30.14(iv), §30.14(v)
Permalink:: http://dlmf.nist.gov/30.13.E13
Encodings:: pMML, png, TeX
See also:: Annotations for §30.13(iv), §30.13 and Ch.30

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30.13.14

w_{1}(\xi)=a_{1}S^{m(1)}_{n}\left(\xi,\gamma\right)+b_{1}S^{m(2)}_{n}\left(\xi% ,\gamma\right).

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Symbols:: $S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},\NVar{\gamma}\right)$ : radial spheroidal wave function, $m$ : nonnegative integer, $n\geq m$ : integer degree, $\xi$ : prolate spheroidal coordinate, $b_{j}$ : coefficients, $w_{j}$ : solution to DE, $\gamma^{2}=\kappa^{2}c^{2}$ : parameter and $a_{j}$ : coefficients
Referenced by:: §30.13(v)
Permalink:: http://dlmf.nist.gov/30.13.E14
Encodings:: pMML, png, TeX
See also:: Annotations for §30.13(iv), §30.13 and Ch.30

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30.13.15

S^{m(1)}_{n}\left(\xi_{0},\gamma\right)=0.

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Symbols:: $S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},\NVar{\gamma}\right)$ : radial spheroidal wave function, $m$ : nonnegative integer, $n\geq m$ : integer degree, $\xi$ : prolate spheroidal coordinate and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.13.E15
Encodings:: pMML, png, TeX
See also:: Annotations for §30.13(v), §30.13 and Ch.30

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34: Bibliography M

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J. W. Miles (1975) Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.

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External Links:: MathReview (M. L. Mehta), ZentralBlatt
Referenced by:: §30.9(i).
Encodings:: BibTeX

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H. J. W. Müller (1962) Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 211, pp. 33–47.

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External Links:: MathReview (J. Meixner), ZentralBlatt
Referenced by:: §30.9(ii), §30.9(ii).
Encodings:: BibTeX

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H. J. W. Müller (1966a) Asymptotic expansions of ellipsoidal wave functions and their characteristic numbers. Math. Nachr. 31, pp. 89–101.

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External Links:: Document, MathReview (F. M. Arscott), ZentralBlatt
Referenced by:: §29.11, §29.7(i), §29.7(ii).
Encodings:: BibTeX

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H. J. W. Müller (1966b) Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions. Math. Nachr. 32, pp. 49–62.

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External Links:: Document, MathReview (M. J. O. Strutt), ZentralBlatt
Referenced by:: §29.11, §29.7(ii).
Encodings:: BibTeX

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H. J. W. Müller (1966c) On asymptotic expansions of ellipsoidal wave functions. Math. Nachr. 32, pp. 157–172.

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External Links:: Document, MathReview (F. M. Arscott), ZentralBlatt
Referenced by:: §29.11, §29.7(ii).
Encodings:: BibTeX

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35: Bibliography S

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M. J. Seaton and G. Peach (1962) The determination of phases of wave functions. Proc. Phys. Soc. 79 (6), pp. 1296–1297.

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External Links:: Document, ZentralBlatt
Referenced by:: §33.23(vii).
Encodings:: BibTeX

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M. J. Seaton (2002b) FGH, a code for the calculation of Coulomb radial wave functions from series expansions. Comput. Phys. Comm. 146 (2), pp. 250–253.

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Notes:: Single-precision Fortran code.
External Links:: Document, Code, ZentralBlatt
Referenced by:: 10th item.
Encodings:: BibTeX

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B. D. Sleeman (1968a) Integral equations and relations for Lamé functions and ellipsoidal wave functions. Proc. Cambridge Philos. Soc. 64, pp. 113–126.

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External Links:: Document, MathReview (Y. L. Luke), ZentralBlatt
Referenced by:: §29.8.
Encodings:: BibTeX

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D. Slepian and H. O. Pollak (1961) Prolate spheroidal wave functions, Fourier analysis and uncertainty. I. Bell System Tech. J. 40, pp. 43–63.

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External Links:: MathReview (I. Marx), ZentralBlatt
Referenced by:: §30.15(v).
Encodings:: BibTeX

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D. Slepian (1964) Prolate spheroidal wave functions, Fourier analysis and uncertainity. IV. Extensions to many dimensions; generalized prolate spheroidal functions. Bell System Tech. J. 43, pp. 3009–3057.

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External Links:: ISSN 0005-8580, MathReview (J. Meixner), ZentralBlatt
Referenced by:: §30.12.
Encodings:: BibTeX

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36: 18.39 Applications in the Physical Sciences

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a) Spherical Radial Coulomb Wave Functions Expressed in terms of Laguerre OP’s

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c) Spherical Radial Coulomb Wave Functions

… ►The radial Coulomb wave functions

R_{n,l}(r)

, solutions of … ►

d) Radial Coulomb Wave Functions Expressed in Terms of the Associated Coulomb–Laguerre OP’s

… ►The Coulomb–Pollaczek polynomials provide alternate representations of the positive energy Coulomb wave functions of Chapter 33. …

37: Bibliography I

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Y. Ikebe (1975) The zeros of regular Coulomb wave functions and of their derivatives. Math. Comp. 29, pp. 878–887.

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External Links:: ISSN 0025-5718, Document, MathReview, ZentralBlatt
Referenced by:: §3.8(iii).
Encodings:: BibTeX

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38: 31.17 Physical Applications

… ►More applications—including those of generalized spheroidal wave functions and confluent Heun functions in mathematical physics, astrophysics, and the two-center problem in molecular quantum mechanics—can be found in Leaver (1986) and Slavyanov and Lay (2000, Chapter 4). For application of biconfluent Heun functions in a model of an equatorially trapped Rossby wave in a shear flow in the ocean or atmosphere see Boyd and Natarov (1998).

39: Bibliography B

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T. A. Beu and R. I. Câmpeanu (1983a) Prolate angular spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 187–192.

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External Links:: Document, Code
Referenced by:: 1st item.
Encodings:: BibTeX

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T. A. Beu and R. I. Câmpeanu (1983b) Prolate radial spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 177–185.

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External Links:: Document, Code
Referenced by:: 1st item.
Encodings:: BibTeX

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I. Bloch, M. H. Hull, A. A. Broyles, W. G. Bouricius, B. E. Freeman, and G. Breit (1950) Methods of calculation of radial wave functions and new tables of Coulomb functions. Physical Rev. (2) 80, pp. 553–560.

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External Links:: Document, MathReview (S. C. van Veen), ZentralBlatt
Referenced by:: §33.7.
Encodings:: BibTeX

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C. J. Bouwkamp (1947) On spheroidal wave functions of order zero. J. Math. Phys. Mass. Inst. Tech. 26, pp. 79–92.

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External Links:: ISSN 0097-1421, MathReview (M. J. O. Strutt), ZentralBlatt
Referenced by:: §30.16(i).
Encodings:: BibTeX

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A. Burgess (1963) The determination of phases and amplitudes of wave functions. Proc. Phys. Soc. 81 (3), pp. 442–452.

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External Links:: Document
Referenced by:: §33.23(vii).
Encodings:: BibTeX

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40: Bibliography F

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P. Falloon (2001) Theory and Computation of Spheroidal Harmonics with General Arguments. Master’s Thesis, The University of Western Australia, Department of Physics.

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Notes:: Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.
External Links:: FullText
Referenced by:: §30.12, 1st item, 2nd item.
Encodings:: BibTeX

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C. Flammer (1957) Spheroidal Wave Functions. Stanford University Press, Stanford, CA.

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External Links:: MathReview (J. C. P. Miller), ZentralBlatt
Referenced by:: §30.1, §30.10, 2nd item, Ch.30.
Encodings:: BibTeX

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C. Fröberg (1955) Numerical treatment of Coulomb wave functions. Rev. Mod. Phys. 27 (4), pp. 399–411.

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External Links:: Document, MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: §33.10(ii), §33.11, §33.12(i), §33.9(ii).
Encodings:: BibTeX

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