With an improved Numerov algorithm, continuum state wave functions and its normalization are investigated. Cowan' s normalization is discussed and a more precise and effective calculation is offered. We calculate the Thomas-Reiche-Kuhn(TRK) sum of several hydrogen atomic states (l=0~3). The least-squared method is used to generate infinite asymptotical forms of TRK. The residues are approximately calculated with an integral processing.

We consider the problem of constructing artificial boundary conditions for the wave equation. Two new boundary conditions are presented directly by a difference approximation. The stability of these boundary conditions and their consistency with the analytical boundary conditions are proved. Numericl examples indicate that these boundary conditions work effectively.