A kind regularization method for solving Cauchy problem of the Schrödinger equation

The potential-free field Schrödinger Cauchy problem is the major topic of this research. Because it is gravely ill-posed in the Hadamard sense. The Cauchy problem is modified through an improved boundary method. The regular approximate solution is created based on the priori and posteriori regularization parameter selection rules, and the convergence evidence is provided. The proposed method is practical under the priori and the posteriori regularization methods, according to numerical experiments. It works well and is resistant to data disruption noise.