Exploring a discretized generator coordinate route to approximate eigenstates of one- and two-dimensional anharmonic oscillators within the framework of the simulated annealing method

A discretized generator coordinate based recipe is explored for finding eigenstates of one and two dimensional anharmonic oscillators. The resulting non-linear variational problem is handled by invoking the method of simulated annealing as a stochastic minimizer. The ground and a few excited state eigenvalues are obtained either by sequential or manifold energy minimization routes. From the optimized eigenvalues and eigenvectors, we explore the possibility of constructing a suitable unperturbed Hamiltonian H(0) around which a faster convergent perturbative expansion can be carried out.