Schrödinger-type identity for Schrödinger free boundary problems

Our aim in this paper is to develop a Schrodinger-type identity for a Schrodinger free boundary problem in \(\mathbb{R}^{n}\). As an application, we establish necessary and sufficient conditions for the product of some distributional functions to satisfy the Schrodinger-type identity. As a consequence, our results significantly improve and generalize previous work.