Quantum confinement detection using a coupled Schrödinger system

Abstract

Machine learning techniques have provided valuable insights into understanding the fundamental principles of physics. Recent studies have demonstrated the ability of deep neural networks (DNNs) to learn a wide range of differential equations (DEs) and classical Hamiltonian mechanics systems. This has led to the emergence of solving the inverse problem associated with partial differential equations using DNNs. In this paper, we propose a novel method for detecting quantum confinement by numerically solving the Schrödinger system on manifolds with nonlinear coupling. Our method exhibits remarkable performance in identifying various quantum phenomena. Moreover, our research introduces a promising approach for principled modeling and prediction in quantum processes. By combining deep learning with traditional models, our hybrid model leverages the strengths of both approaches, enhancing computational efficiency and enabling meaningful predictions for complex quantum physical processes. The integration of multiple deep learning principles with quantum physics enables effective handling of large datasets and addresses inverse challenges related to intricate dynamical systems and physical phenomena.