Coulomb%20phase%20shift
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1: 33.24 Tables
§33.24 Tables
►Abramowitz and Stegun (1964, Chapter 14) tabulates , , , and for and , 5S; for , 6S.
2: 33.25 Approximations
§33.25 Approximations
►Cody and Hillstrom (1970) provides rational approximations of the phase shift (see (33.2.10)) for the ranges , , and . …3: 33.2 Definitions and Basic Properties
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§33.2(i) Coulomb Wave Equation
… ► is the Coulomb phase shift. … ►Also, are analytic functions of when . ►§33.2(iv) Wronskians and Cross-Product
…4: 33.13 Complex Variable and Parameters
§33.13 Complex Variable and Parameters
►The functions , , and may be extended to noninteger values of by generalizing , and supplementing (33.6.5) by a formula derived from (33.2.8) with expanded via (13.2.42). … ►The quantities , , and , given by (33.2.6), (33.2.10), and (33.4.1), respectively, must be defined consistently so that ►
33.13.1
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33.13.2
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5: 33.3 Graphics
§33.3 Graphics
►§33.3(i) Line Graphs of the Coulomb Radial Functions and
… ► … ►§33.3(ii) Surfaces of the Coulomb Radial Functions and
… ►6: 33.5 Limiting Forms for Small , Small , or Large
7: 33.23 Methods of Computation
§33.23 Methods of Computation
… ►The methods used for computing the Coulomb functions described below are similar to those in §13.29. … ►Combined with the Wronskians (33.2.12), the values of , , and their derivatives can be extracted. … ►§33.23(vii) WKBJ Approximations
… ►Hull and Breit (1959) and Barnett (1981b) give WKBJ approximations for and in the region inside the turning point: .8: 33.10 Limiting Forms for Large or Large
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§33.10(i) Large
… ►where is defined by (33.2.9). ►§33.10(ii) Large Positive
… ►§33.10(iii) Large Negative
…9: 33.11 Asymptotic Expansions for Large
§33.11 Asymptotic Expansions for Large
… ►where is defined by (33.2.9), and and are defined by (33.8.3). … ►10: William P. Reinhardt
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►Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions.
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.