Coulomb wave function
Encyclopedia
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 function
s or Whittaker function
s of imaginary argument.
where L is usually a non-negative integer. The solutions are called Coulomb wave functions. Putting x = 2iρ changes the Coulomb wave equation into the Whittaker equation, so Coulomb wave functions can be expressed in terms of Whittaker functions with imaginary arguments.
Two special solutions called the regular and irregular Coulomb wave functions are denoted by FL(η,ρ) and GL(η,ρ), and defined in terms of the confluent hypergeometric function
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Charles-Augustin de Coulomb
Charles-Augustin de Coulomb was a French physicist. He is best known for developing Coulomb's law, the definition of the electrostatic force of attraction and repulsion. The [SI unit] of charge, the coulomb, was named after him....
. They are used to describe the behavior of charged particles in a Coulomb potential and can be written in terms of confluent hypergeometric function
Confluent hypergeometric function
In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity...
s or Whittaker function
Whittaker function
In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by to make the formulas involving the solutions more symmetric...
s of imaginary argument.
Coulomb wave equation
The Coulomb wave equation iswhere L is usually a non-negative integer. The solutions are called Coulomb wave functions. Putting x = 2iρ changes the Coulomb wave equation into the Whittaker equation, so Coulomb wave functions can be expressed in terms of Whittaker functions with imaginary arguments.
Two special solutions called the regular and irregular Coulomb wave functions are denoted by FL(η,ρ) and GL(η,ρ), and defined in terms of the confluent hypergeometric function
Confluent hypergeometric function
In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity...
by