물리지식기반 인공신경망을 이용한 가우시안 형태의 양자 퍼텐셜의 고유치 문제 풀이

In this study, we solved the eigenfunction and eigenvalue problems of the Schr¨odinger equation with a Gaussian potential, which plays an important role in both theoretical and experimental contexts, using Physics-Informed Neural Networks (PINNs). Since the Gaussian potential lacks an analytical solution, we validated the results obtained from PINNs using the fnite diference method. The results showed that PINNs closely matched the fnite diference method for the ground state and lower energy levels, with eigenvalues agreeing within a 1% margin of error. However, at higher energy levels, discrepancies arose due to boundary conditions and the limitations of the orthogonality loss function. This study demonstrates the potential of applying PINNs to eigenvalue problems in realistic experimental scenarios and discusses their possible use in future research on complex quantum systems and as an educational tool.