A new adaptive delta potential crossover operator, one process of the improved genetic algorithm, is proposed in this paper to overcome the drawbacks of high randomness and slow convergence speed of genetic algorithm. The new crossover operator is based on the reflectance and transmittance coefficients of particle penetrating the delta potential in quantum mechanics. The improved genetic algorithm, which is used in neural network training, includes the new crossover operator and the deterministic crowding mechanism. It has been demonstrated by simulation results and the pattern recognition experiment on blue-green algae that the approach not only has the properties of high convergence speed and good searching ability but also has efficiency in pattern recognition