Coulomb wave function

In mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe the behavior of charged particles in a Coulomb potential and can be written in terms of confluent hypergeometric functions or Whittaker functions of imaginary argument.

The Coulomb wave equation for a single charged particle is the Schrödinger equation with Coulomb potential

where ${\displaystyle Z=Z_{1}Z_{2}}$ is the product of the charges of the particle and of the field source (in units of the elementary charge, ${\displaystyle Z=-1}$ for hydrogen atom) and ${\displaystyle k^{2}}$ is proportional to the asymptotic energy of the particle. The solution – Coulomb wave function – can be found by solving this equation in parabolic coordinates

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