Supersingular potentials are defined as potentials involving derivatives of the delta function of order higher than one. In this work we solve the Schrödinger equation for supersingular potentials. For the bound states, we calculate their energy and the corresponding wave functions (when they exist). For the scattering state we calculate the reflection and transmission coefficients in addition to the wave function of these states. We study the case of the delta double prime potential in details, showing that we may have none, one or two bound states, depending on the relations between the values of the coupling constants. In general the wave function in the position space has discontinuity at the point of support of the supersingular potential.

超奇异势被定义为涉及高于一阶的 delta 函数的导数的势。在这项工作中，我们解决了超奇异势的薛定谔方程。对于束缚态，我们计算它们的能量和相应的波函数（当它们存在时）。对于散射状态，除了这些状态的波函数之外，我们还计算反射和透射系数。我们详细研究了 delta 双素势的情况，表明我们可能没有、一个或两个束缚态，这取决于耦合常数值之间的关系。通常，位置空间中的波函数在超奇异势的支撑点处具有不连续性。