  In this paper, we study 1-d random Schr\"odinger operators on a finite
interval with Dirichlet boundary conditions. We are interested in the
approximation of the ground state energy using the minimum of the effective
potential. For the 1-d continuous Anderson Bernoulli model, we show that the
ratio of the ground state energy and the minimum of the effective potential
approaches $\frac{\pi^2}{8}$ as the domain size approaches infinity. Besides,
we will discuss various approximations to the ratio in different situations.
There will be numerical experiments supporting our main results for the ground
state energy and also supporting approximations for the excited states
energies.
