Uniqueness of Solution of an Inverse Problem for the Quantum Kinetic Equation

Abstract

This study focuses on an inverse problem for the quantum kinetic equations, the cornerstone of quantum mechanics. These equations describe the evolution of elementary particles under strong interactions. They are fundamental to understanding the behavior of quantum systems and play a pivotal role in describing nanostructure processes and nanodiagnostics. The main target of the problem is to determine the unknown source function on the right-hand side of the equation. This paper obtains a pointwise Carleman estimate. It then uses the Carleman estimate to show the uniqueness of the problem's solution.

Keywords

• Quantum kinetic equation
• inverse problem
• uniqueness of the solution
• pointwise Carleman estimate

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