  Quantum theory has been remarkably successful in providing an understanding
of physical systems at foundational scales. Solving the Schr\"odinger equation
provides full knowledge of all dynamical quantities of the physical system.
However closed form solutions to this equation are only available for a few
systems and approximation methods are typically used to find solutions. In this
paper we address the problem of solving the time independent Schr\"odinger
equation for the ground state solution of physical systems. We propose using
end-to-end deep learning approach in a variational optimization scheme for
approximating the ground state energies and wave functions of these systems. A
neural network realizes a universal trial wave function and is trained in an
unsupervised learning framework by optimizing the expectation value of the
Hamiltonian of a physical system. The proposed approach is evaluated on
physical systems consisting of a particle in a box with and without a
perturbation. We demonstrate that our approach obtains approximations of ground
state energies and wave functions that are highly accurate, which makes it a
potentially plausible candidate for solving more complex physical systems for
which analytical solutions are beyond reach.
