\begin{document}$F(x) = \int_{-\infty}^{x} \psi^*\psi {\rm d}x'$\end{document}. Using this constrained neural network to represent the variational wave function, we solve Schrodinger equations using auto-differentiation and stochastic gradient descent (SGD) by minimizing the violation of the trial wave function \begin{document}$ \psi(x) $\end{document} to the Schrodinger equation. For several classical problems in quantum mechanics, we obtain their ground state wave function and energy with very low errors. The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future."> Solving Schrodinger equations using a physically constrained neural network -
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