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Absorbing boundary conditions for solving N-dimensional stationary Schrodinger equations with unbounded potentials and nonlinearities. Applications to ground states computations

We propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrodinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrequations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrodinger equations.