2010/10/13 by Asaf Shimshovitz, Shimshovitz, Asaf, David J. Tannor +1 · 1 citation
Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Model Reduction and Neural Networks #Quantum Physics (quant-ph) #Scientific Research and Discoveries #Spectroscopy and Quantum Chemical Studies #physics.comp-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.1010.2588
5 pages, 5 figures
arxiv created 2010/10/13 · openalex publication_date 2010/10/13 · arxiv updated 2010/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new method for solving quantum mechanical problems, which combines the flexibility of Gaussian basis set methods with the numerical accuracy of the Fourier method. The method is based on the incorporation of periodic boundary conditions into the von Neumann basis of phase space Gaussians [F. Dimler et al., New J. Phys. 11, 105052 (2009)]. In this paper we focus on the Time-independent Schrödinger Equation and show results for the harmonic, Morse and Coulomb potentials that demonstrate that the periodic von Neumann method or pvN is significantly more accurate than the usual vN method. Formally, we are able to show an exact equivalence between the pvN and the Fourier Grid Hamiltonian (FGH) methods. Moreover, due to the locality of the pvN functions we are able to remove Gaussian basis functions without loss of accuracy, and obtain significantly better efficiency than that of the FGH. We show that in the classical limit the method has the remarkable efficiency of 1 basis function per 1 eigenstate.