Numerical solutions of the Schrِdinger equation directly or perturbatively by a genetic algorithm: test cases

The workability of a genetic algorithm-based strategy to solve the Schrödinger equation directly is tested with reference to a screened Coulomb potential and an oscillator with quartic anharmonicity. The suitability of the same basic idea in solving the inhomogeneous differential equations of Rayleigh–Schrödinger perturbation theory is also examined in this context with particular reference to the ground state of a two-electron atom. Special advantages of the general approach are stressed.