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

We present a new method based on evolutionary algorithms which permits to d etermine efficiently the ground state of the time-independent Schrodinger e quation for arbitrary external potentials. The approach relies on the varia tional principle. The ground-state wave function of a given Hamiltonian is found by using the procedure of survival of the fittest, starting from a po pulation of wave functions. To perform the search for the fittest wave func tion we have extended a genetic algorithm to treat quantum mechanical probl ems. We present results for different one dimensional external potentials a nd compare them with analytical solutions and with other numerical methods. Our approach yields very good convergence in all cases, Potential applicat ions of the quantum genetic algorithm presented here to more dimensions and many-body problems are discussed. (C) 2000 Elsevier Science B.V. All right s reserved.