连续态数值波函数归一化的近似计算及TRK求和中余项的积分处理

Approximate Normalization of Numeric Continuum State Wave Functions and Integral Processing of Residues in TRK Sums

采用改进的Numerov格式，对连续态波函数及其归一化问题作了细致的计算．指出了Cowan在ε→0时状态波函数的归一化中存在的问题，给出了更加准确、有效的归一化计算方法．为了检验这一算法，计算了氢原子各状态（l=0.3）下的Thomas-Reiche—Kuhn（TRK）和．利用最小二乘法，给出了TRK求和中无穷项的渐近函数形式，并由此采用积分方法得到了余项的近似计算结果．

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.