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31: 31.17 Physical Applications

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32: Bibliography O

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A closed form solution of the $s$-wave Bethe-Goldstone equation with an infinite repulsive core. J. Math. Phys. 27 (4), pp. 1154–1158.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§30.13(v).

Encodings:

BibTeX

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33: 30.6 Functions of Complex Argument

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34: 20.13 Physical Applications

… ►This allows analytic time propagation of quantum wave-packets in a box, or on a ring, as closed-form solutions of the time-dependent Schrödinger equation.

35: 30.9 Asymptotic Approximations and Expansions

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36: Bibliography K

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The Korteweg-de Vries Equation and Related Evolution Equations. In Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972), A. C. Newell (Ed.), Lectures in Appl. Math., Vol. 15, pp. 61–83.

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External Links:

MathReview (G. L. Lamb, Jr.), ZentralBlatt

Referenced by:

§22.19(iii).

Encodings:

BibTeX

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37: 18.39 Applications in the Physical Sciences

… ► $\mathscr{H}$ also controls time evolution of the wave function $\mathrm{\Psi }(x,t)$ via the time-dependent Schrödinger equation, … ►Substitution of (18.39.24) into (18.39.23) then gives the ordinary differential equation for the radial wave function $R_{n,l}(r)$, … ►(where the minus sign is often omitted, as it arises as an arbitrary phase when taking the square root of the real, positive, norm of the wave function), allowing equation (18.39.37) to be rewritten in terms of the associated Coulomb–Laguerre polynomials ${𝐋}_{n+l}^{2l+1}({\rho }_n)$. … ►

Discretized and Continuum Expansions of Scattering Eigenfunctions in terms of Pollaczek Polynomials: J-matrix Theory

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38: 30.12 Generalized and Coulomb Spheroidal Functions

… ►Generalized spheroidal wave functions and Coulomb spheroidal functions are solutions of the differential equation …

39: 28.31 Equations of Whittaker–Hill and Ince

§28.31 Equations of Whittaker–Hill and Ince

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§28.31(iii) Paraboloidal Wave Functions

►With (28.31.10) and (28.31.11), …are called paraboloidal wave functions. … ►

Asymptotic Behavior

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40: 31.18 Methods of Computation

… ►The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.