attractive potentials

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1: 33.22 Particle Scattering and Atomic and Molecular Spectra

… â–ºAt positive energies

E>0

\rho\geq 0

, and: â–º â–º â–º

Attractive potentials:	$Z_{1}Z_{2}<0$ , $\eta<0$ .
…

… â–º

R_{\infty}=m_{e}c{\alpha}^{2}/(2\hbar)

. â–º â–º â–º

Attractive potentials:	$Z_{1}Z_{2}<0$ , $r>0$ .
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… â–º â–º â–º

Attractive potentials:	$Z_{1}Z_{2}<0$ , $\Im\kappa<0$ .
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2: Bibliography B

… â–º

E. Bank and M. E. H. Ismail (1985) 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:: BibTeX

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3: Bibliography S

… â–º

M. J. Seaton (2002a) 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.
Encodings:: BibTeX

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4: 18.39 Applications in the Physical Sciences

… â–ºThe Schrödinger equation with potential … â–ºBound state solutions to the relativistic Dirac Equation, for this same problem of a single electron attracted by a nucleus with

Z

protons, involve Laguerre polynomials of fractional index. … â–ºThese cases correspond to the two distinct orthogonality conditions of (18.35.6) and (18.35.6_3). … â–ºIn the attractive case (18.35.6_4) for the discrete parts of the weight function where with

x_{k}<-1

, are also simplified: …The weight functions for both the attractive and repulsive cases are now unit normalized, see Bank and Ismail (1985), and Ismail (2009). …