Abstract
In this paper the Lagrange-mesh method is used to solve the two- and three-dimensional Schrödinger equation in spherical coordinates. Matrix elements that involve few free parameters and depend on the grid points for the Hamiltonian, and can be used with any quantum mechanical system, are employed. The accuracy of the matrix elements is tested with the quartic anharmonic oscillator and a double ring-shaped harmonic oscillator potentials. Eigenvalues for the systems are reproduced to within machine accuracy when the free parameters of the matrix elements are chosen appropriately.
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