An evolutionary algorithm to calculate the ground state of a quantum system

We present a new method based on evolutionary algorithms which permits to determine efficiently the ground state of the time-independent Schrödinger equation for arbitrary external potentials. The approach relies on the variational principle. The ground-state wave function of a given Hamiltonian is found by using the procedure of survival of the fittest, starting from a population of wave functions. To perform the search for the fittest wave function we have extended a genetic algorithm to treat quantum mechanical problems. We present results for different one dimensional external potentials and compare them with analytical solutions and with other numerical methods. Our approach yields very good convergence in all cases. Potential applications of the quantum genetic algorithm presented here to more dimensions and many-body problems are discussed.