On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions
This paper studies the stationary Schrödinger equation \[ (\vec \nabla\cdot \vec\nabla +\lambda^2_0) \psi(\vec r)-q (\vec r,\psi, \vec\nabla \psi)=0\text{ in }\mathbb{R}^n, \tag{1} \] with finite potential \(q\). The method of pseudopotential, often used for the study of (1), is contained in replacement of the potential \(q\) by the pseudopotential \(\widehat q\), which does not depend explicitly on \(\psi\) and \(\vec\nabla\psi\). Here in contrast to methods of pseudopotential used up to now, the new method proposed does not require the knowledge of the explicit form of the potential \(q\).
scientific article; zbMATH DE number 1750370