In this work, we follow the Green’s functions technique used by Atkinson and Crater (1975 Am. J. Phys. 43 301–304) to construct a solution of the one-dimensional Schrdinger equation with the delta derivative potential λδ′(x), λ being the coupling constant. The bound and the scattering states solutions were built using the complete set of eigenfunctions of the problem without the delta derivative potential. We defined generalized averages of the wave function and its first derivative to extend the usual definition of the product of δ′(x) with a test function. Explicit expressions for the wave functions were obtained. For the scattering case, the transmission probabilities are found to be energy and coupling constant λ dependent.

在这项工作中，我们遵循 Atkinson 和 Crater (1975 Am. J. Phys. 43 301–304)使用的格林函数技术来构造具有 delta 导数势λδ '( x )的一维Schrdinger方程的解，λ是耦合常数。边界和散射状态解是使用问题的完整特征函数集构建的，没有 delta 导数势。我们定义了波函数的广义平均值及其一阶导数，以扩展δ ′( x) 具有测试功能。获得了波函数的显式表达式。对于散射情况，发现传输概率与能量和耦合常数λ相关。