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1: 14.31 Other Applications
§14.31(iii) Miscellaneous
2: 33.22 Particle Scattering and Atomic and Molecular Spectra
For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, F ( η , ρ ) and G ( η , ρ ) , or f ( ϵ , ; r ) and h ( ϵ , ; r ) , to determine the scattering S -matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951). …
3: 12.17 Physical Applications
Problems on high-frequency scattering in homogeneous media by parabolic cylinders lead to asymptotic methods for integrals involving PCFs. …
4: 18.39 Applications in the Physical Sciences
The Quantum Coulomb Problem: Scattering States
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 . …
5: William P. Reinhardt
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. …
6: Bibliography B
  • W. G. C. Boyd (1973) The asymptotic analysis of canonical problems in high-frequency scattering theory. II. The circular and parabolic cylinders. Proc. Cambridge Philos. Soc. 74, pp. 313–332.
  • 7: 29.19 Physical Applications
    §29.19(ii) Lamé Polynomials
    8: 10.73 Physical Applications
    Accordingly, the spherical Bessel functions appear in all problems in three dimensions with spherical symmetry involving the scattering of electromagnetic radiation. …
    9: Brian D. Sleeman
     thesis was Some Boundary Value Problems Associated with the Heun Equation. Sleeman published numerous papers in applied analysis, multiparameter spectral theory, direct and inverse scattering theory, and mathematical medicine. …
    10: 28.33 Physical Applications
    §28.33(ii) Boundary-Value Problems
    Physical problems involving Mathieu functions include vibrational problems in elliptical coordinates; see (28.32.1). …
    §28.33(iii) Stability and Initial-Value Problems
    References for other initial-value problems include: …
  • Aly et al. (1975) for scattering theory.