2D nondirect product discrete variable representation for Schrödinger equation with nonseparable angular variables. (16th March 2020)

• Record Type: Journal Article
• Authors: Shadmehri, Sara; Saeidian, Shahpoor; Melezhik, Vladimir S
• Is Part Of: Journal of physics. Volume 53:Number 8(2020:Apr. 15)
• Publication Date: 2020-03-16
• Subjects: discrete variable representation -- Lebedev quandratures on unit sphere -- nondirect product grid -- Schrodinger equation with nonseparable angular variables -- spherical functions; Atoms -- Periodicals; Molecules -- Periodicals; Optics -- Periodicals; Nuclear physics -- Periodicals; 539.6
• DOI: 10.1088/1361-6455/ab707b
• Languages: English
• ISSNs: 0953-4075

Abstract

Abstract: We develop a nondirect product discrete variable representation (npDVR) for treating quantum dynamical problems which involve nonseparable angular variables. The npDVR basis is constructed on spherical functions orthogonalized on the grids of the Lebedev or Popov 2D quadratures for the unit sphere instead of the direct product of 1D quadrature rules. We compare our computational scheme with the old one that used the product of 1D Gaussian quadratures in terms of their convergence and efficiency by calculating, as an example, the spectrum of a hydrogen atom in the magnetic and electric fields arbitrarily oriented to one another. The use of the npDVR based on the Lebedev or Popov 2D quadratures substantially accelerates the convergence of the computational scheme. Moreover, we get the fastest convergence with the npDVR based on the Popov quadratures, which has the largest efficiency coefficient.