Lagrange-mesh solution of the Schrödinger equation in generalized spherical coordinates

The solution of themulti-dimensional Schrödinger equation in the generalized spherical coordinates is constructed in the Lagrange-meshmethod. Laguerre and Jacobimeshes are used to constructmatrix elements for the generalizedHamiltonian. Thematrix elements are functions of quadrature abscissas and involve few free parameters for each angular dimension. A ring-shaped non-central separable potential, and a systemof four linearly coupled anharmonic oscillators are used for illustrations of the efficiency and accuracy of themethod. The numerical solutions involving eigenfunctions of the kinetic energy operator display the typical slow convergence with the accuracy improving as the Lagrangemesh bases size increases. The Lagrange-mesh solutions converge to the exact solutionwhen the parameters of thematrix elements are chosen appropriately.