Coulomb potentials

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1: 17.17 Physical Applications

… ►See Kassel (1995). … ►It involves $q$-generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials. …

2: 33.22 Particle Scattering and Atomic and Molecular Spectra

… ►At positive energies $E>0$, $\rho \ge 0$, and: … ► $R_{\mathrm{\infty }}=m_{\mathrm{e}}c{\alpha }^2/(2\mathrm{\hslash })$. … ►

$\kappa =\mathrm{i}{Z}_1{Z}_2\alpha c{(m/(2E))}^{1/2}.$

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§33.22(vi) Solutions Inside the Turning Point

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3: Bibliography H

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Soft-core Coulomb potentials and Heun’s differential equation. J. Math. Phys. 51 (2), pp. Art. ID 022107, 19 pages.

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External Links:

ISSN 0022-2488, Document, FullText, MathReview, ZentralBlatt

Referenced by:

§31.17(ii), §31.17(ii).

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4: Bibliography B

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The attractive Coulomb potential polynomials. Constr. Approx. 1 (2), pp. 103–119.

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External Links:

ISSN 0176-4276, Document, Link, MathReview (W. A. Al-Salam)

Referenced by:

§18.39(iv), §18.39(iv).

Encodings:

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5: Bibliography C

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On the expansion of a Coulomb potential in spherical harmonics. Proc. Cambridge Philos. Soc. 46, pp. 626–633.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§34.12.

Encodings:

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6: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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Example 2: Radial 3D Schrödinger operators, including the Coulomb potential

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7: 18.39 Applications in the Physical Sciences

… ►The positive energy (scattering) eigenfunctions for the above Coulomb problem, with potential $V(r)=-Z{e}^2/r$ are discussed in Chapter 33 for each integer $l$. …

8: Bibliography S

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Coulomb functions for attractive and repulsive potentials and for positive and negative energies. Comput. Phys. Comm. 146 (2), pp. 225–249.

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External Links:

ISSN 0010-4655, Document, MathReview, ZentralBlatt

Referenced by:

§1.17(ii), §33.1, §33.14(i), §33.14(ii), §33.14(iii), §33.14(iv), §33.14(v), §33.16(i), §33.16(ii), §33.16(iii), §33.16(v), §33.17, §33.19, §33.20(i), §33.20(ii), §33.20(iii), §33.21(i), Ch.33.

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9: 13.28 Physical Applications

… ►For potentials in quantum mechanics that are solvable in terms of confluent hypergeometric functions see Negro et al. (2000). … ►

§13.28(ii) Coulomb Functions

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10: Bibliography D

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Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.

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External Links:

Document

Referenced by:

§15.18.

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Supersymmetry, shape invariance, and exactly solvable potentials. Amer. J. Phys. 56, pp. 163–168.

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Referenced by:

§18.38(iii).

Encodings:

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Coulomb wave functions with complex values of the variable and the parameters. J. Math. Phys. 40 (12), pp. 6145–6166.

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External Links:

ISSN 0022-2488, Document, MathReview (Raj Wilson), ZentralBlatt

Referenced by:

§33.13.

Encodings:

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