Coulomb wavefunctions are solutions of the Schrödinger equation for scattering of charged particles by a positively charged nucleus, described by a Coulomb potential. They are important for applications in the quantum theory of scattering, particularly for nuclear physics. Coulomb wavefunctions can be expressed in terms of confluent hypergeometric functions or, alternatively, Whittaker functions. Two special solutions, called the regular and irregular Coulomb wavefunctions, according to their analytic behavior at the nucleus, are denoted by and , respectively.

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[3] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds., NIST Handbook of Mathematical Functions, New York: Cambridge University Press, 2010.