Exact solution to the Coulomb wave using the linearized phase-amplitude method
Exact solution to the Coulomb wave using the linearized phase-amplitude method
复制标题
使用线性化相位振幅法精确求解库仑波
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Kiyokawa
中科院分区：
文献类型：
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作者：
S. Kiyokawa
作者表明，计算连续波函数的相位振幅法的振幅方程可以线性化为三阶微分方程。使用这个线性化方程，在库仑势的情况下，作者还表明幅度函数具有由不规则汇合超几何函数表示的解析精确解。此外，还表明库仑势的精确解再现了由球贝塞尔函数表示的自由空间波函数。狄拉克旋量大分量的振幅方程也被证明是线性化的三阶微分方程。
The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.