Coulomb wave equation
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1: 33.2 Definitions and Basic Properties
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§33.2(i) Coulomb Wave Equation
…2: 33.14 Definitions and Basic Properties
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§33.14(i) Coulomb Wave Equation
…3: 33.22 Particle Scattering and Atomic and Molecular Spectra
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§33.22(vi) Solutions Inside the Turning Point
…4: 30.12 Generalized and Coulomb Spheroidal Functions
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►Generalized spheroidal wave functions and Coulomb spheroidal functions are solutions of the differential equation
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5: 31.12 Confluent Forms of Heun’s Equation
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►This has regular singularities at and , and an irregular singularity of rank 1 at .
►Mathieu functions (Chapter 28), spheroidal wave functions (Chapter 30), and Coulomb spheroidal functions (§30.12) are special cases of solutions of the confluent Heun equation.
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6: Bibliography F
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The Lamé wave equation.
Uspekhi Mat. Nauk 44 (1(265)), pp. 123–144, 248 (Russian).
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Spheroidal Wave Functions.
Stanford University Press, Stanford, CA.
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Electromagnetic Diffraction and Propagation Problems.
International Series of Monographs on Electromagnetic Waves,
Vol. 1, Pergamon Press, Oxford.
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Diffraction of radio waves around the earth’s surface.
Acad. Sci. USSR. J. Phys. 9, pp. 255–266.
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Numerical treatment of Coulomb wave functions.
Rev. Mod. Phys. 27 (4), pp. 399–411.
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7: Bibliography H
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Calculation of Coulomb wave functions for high energies.
Phys. Rev. 54 (8), pp. 627–628.
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Coulomb Wave Functions.
In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.),
pp. 408–465.
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Analytical structure and properties of Coulomb wave functions for real and complex energies.
Ann. Physics 155 (2), pp. 461–493.
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Bessel function expansions of Coulomb wave functions.
J. Math. Phys. 26 (4), pp. 656–659.
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The eigenvalues of the angular spheroidal wave equation.
Stud. Appl. Math. 66 (3), pp. 217–240.
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8: Software Index
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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28 Mathieu Functions and Hill’s Equation | |||||||||||||||||||||||||
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30 Spheroidal Wave Functions | |||||||||||||||||||||||||
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30.18(iii) Wave Functions | ✓ | ✓ | ✓ | ✓ | Van Buren | ||||||||||||||||||||
33 Coulomb Functions | |||||||||||||||||||||||||
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9: Bibliography T
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Coulomb functions with complex angular momenta.
Comput. Phys. Comm. 17 (4), pp. 351–355.
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Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations.
Phys. Rev. Lett. 29 (16), pp. 1114–1118.
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COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments.
Comput. Phys. Comm. 36 (4), pp. 363–372.
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Coulomb and Bessel functions of complex arguments and order.
J. Comput. Phys. 64 (2), pp. 490–509.
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Erratum to “COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments”.
Comput. Phys. Comm. 159 (3), pp. 241–242.
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