Exact solution to the Coulomb wave using the linearized phase-amplitude method | Zendy

Shuji Kiyokawa | Zendy

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Exact solution to the Coulomb wave using the linearized phase-amplitude method

Author(s) -

Shuji Kiyokawa

Publication year - 2015

Publication title -

aip advances

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.421

H-Index - 58

ISSN - 2158-3226

DOI - 10.1063/1.4929399

Subject(s) - coulomb wave function , amplitude , bessel function , physics , hypergeometric function , exact differential equation , differential equation , exact solutions in general relativity , mathematical analysis , coulomb , dirac equation , wave equation , helmholtz equation , first order partial differential equation , quantum electrodynamics , quantum mechanics , mathematics , boundary value problem , electron

The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation

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