A new approach for solving the Schrodinger equation based on a microgenetic algorithm (mu-GA) is presented. Feed forward neural network is used to represent the solution, while random point evaluation method (RPEM) is introduced to define the fitness score to be maximized in the mu-GA breeding procedure. Convergence of the final stage of searching is accelerated by invoking the deterministic optimizer. The algorithm is tested in the calculation of one-dimensional harmonic oscillator and double-well potential systems.