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We develop a nondirect product discrete variable representation (npDVR) fortreating quantum dynamical problems which involve nonseparable angularvariables. The npDVR basis is constructed on spherical functions orthogonalizedon the grids of the Lebedev or Popov 2D quadratures for the unit sphere insteadof the direct product of 1D quadrature rules. We compare our computationalscheme with the old one that used the product of 1D Gaussian quadratures interms of their convergence and efficiency by calculating, as an example, thespectrum of a hydrogen atom in the magnetic and electric fields arbitrarilyoriented to one another. The use of the npDVR based on the Lebedev or Popov 2Dquadratures substantially accelerates the convergence of the computationalscheme. Moreover, we get the fastest convergence with the npDVR based on thePopov quadratures, which has the largest efficiency coefficient.

2D Nondirect Product Discrete Variable Representation for Schr\"odinger Equation with Nonseparable Angular Variables