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Quantum theory has been remarkably successful in providing an understandingof physical systems at foundational scales. Solving the Schr\"odinger equationprovides full knowledge of all dynamical quantities of the physical system.However closed form solutions to this equation are only available for a fewsystems and approximation methods are typically used to find solutions. In thispaper we address the problem of solving the time independent Schr\"odingerequation for the ground state solution of physical systems. We propose usingend-to-end deep learning approach in a variational optimization scheme forapproximating the ground state energies and wave functions of these systems. Aneural network realizes a universal trial wave function and is trained in anunsupervised learning framework by optimizing the expectation value of theHamiltonian of a physical system. The proposed approach is evaluated onphysical systems consisting of a particle in a box with and without aperturbation. We demonstrate that our approach obtains approximations of groundstate energies and wave functions that are highly accurate, which makes it apotentially plausible candidate for solving more complex physical systems forwhich analytical solutions are beyond reach.

Approximating Ground State Energies and Wave Functions of Physical Systems with Neural Networks