A mollification regularization method with Dirichlet kernel to solve potential-free field inverse Schrödinger Cauchy problem

Abstract

We consider solving the Cauchy problem of the Schrödinger equation with potential-free field by a mollification regularization method in this work. By convolving the measured data with the Dirichlet kernel, the ill-posed case is turned into a well-posed one. Convergent estimates are gained via the priori and the posteriori parameter selection rules. Finally, three simulation experiment results are shown to prove the feasibility and stability of our presented procedure.

Keywords:

• Inverse Schrödinger equation
• mollification regularization method
• Dirichlet kernel
• potential-free field
• convergence estimates

AMS Subject Classifications:

• 35A22
• 35Q41
• 65M32

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first and second authors are supported in part by National Natural Science Foundation of China (NSFC)  Research Grant (No. 12062024, China) and Graduate Innovation Program of Ningxia University (No. CXXM202319). The third author is supported in part by Construction Project of FirstClass Disciplines in Ningxia Higher Education (NXYLXK202111).