Variational Technique for Scattering Theory
Variational Technique for Scattering Theory
复制标题
散射理论的变分技术
DOI：
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发表时间：
1973
期刊：
影响因子：
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通讯作者：
R. Conn
中科院分区：
文献类型：
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作者：
H. Rabitz;R. Conn
讨论了使用试T矩阵而不是试波函数的T矩阵的平稳变分泛函。将一个试验$T$矩阵表示为矩阵的一般线性组合，得到系数向量的第一类Fredholm积分方程。对于除变系数外与玻恩级数形式相同的试函数的特殊情况，本文作了详细的讨论。在这种试验形式下，要求函数是平稳的，导致先前建立的散射振幅的Pad'e近似结果。采用近似技术计算高阶玻恩积分，并研究了汤川势的Pad’e近似和玻恩级数的性质。该级数的上界用于估计其收敛半径作为能量和势强度的函数。即使在玻恩级数发散的情况下，变分计算也迅速收敛。
A stationary variational functional for the $T$ matrix that uses trial $T$ matrices rather than trial wave functions is discussed. Taking a trial $T$ matrix expressed as a general linear combination of matrices leads to a Fredholm integral equation of the first kind for the coefficient vector. The special case of a trial function having the same form as the Born series, except with variable coefficients, is treated in detail. Requiring the functional to be stationary with this trial form leads to the previously established result of Pad'e approximants to the scattering amplitude. Approximate techniques are used to evaluate the high-order Born integrals, and the behavior of the Pad'e approximants and the Born series is investigated for a Yukawa potential. An upper bound on the series is used to estimate its radius of convergence as a function of energy and potential strength. The variational calculations converge rapidly even for cases where the Born series diverges.