Some integrals involving Coulomb functions associated with the three-dimensional proper Lorentz group

Abstract

For two continual bases in the representation space, we obtain the matrix elements of the linear operator transforming the first basis into the second. These elements are expressed in terms of Coulomb wave functions. Computing the matrix elements of subrepresentations to some subgroups or their separate elements and using the connection between above bases, we evaluate some integrals involving Coulomb wave functions.

Keywords

• coulomb functions
• bessel-clifford functions
• the first and the second bessel-clifford integral transforms
• bessel-macdonald integral transform
• appell function f1
• whittaker function
• proper lorenz group
• bases transformations
• matrix elements of representation