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Coulomb wave functions with complex values of the variable and the parameters. (English) Zbl 0967.81023
Summary: The motivation for the present paper lies in the fact that the literature concerning the Coulomb wave functions F L (η,ρ) and G L (η,ρ) is a jungle in which it may be hard to find a safe way when one needs general formulas for the Coulomb wave functions with complex values of the variable ρ and the parameters L and η. For the Coulomb wave functions and certain linear combinations of these functions we discuss the connection with the Whittaker function, the Coulomb phase shift, Wronskians, reflection formulas (L-L-1), integral representations, series expansions, circuital relations (ρρe ±iπ ) and asymptotic formulas on a Riemann surface for the variable ρ. The parameters L and η are allowed to assume complex values.
MSC:
81Q20Semi-classical techniques in quantum theory, including WKB and Maslov methods
33E15Other wave functions
81Q99General mathematical topics and methods in quantum theory