TY - JOUR
T1 - Phase-space approach to solving the time-independent Schrödinger equation
AU - Shimshovitz, Asaf
AU - Tannor, David J.
N1 - Israel Science FoundationThis work was supported by the Israel Science Foundation and made possible, in part, by the historic generosity of the Harold Perlman family. We thank Bill Poirier for helpful discussions.
PY - 2012/8/17
Y1 - 2012/8/17
N2 - We propose a method for solving the time-independent Schrödinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice, we solve a longstanding problem of convergence of the vN method. This opens the door to tailoring quantum calculations to the underlying classical phase space structure while retaining the accuracy of the Fourier grid basis. The method has the potential to provide enormous numerical savings as the dimensionality increases. In the classical limit, the method reaches the remarkable efficiency of one basis function per one eigenstate. We illustrate the method for a challenging two-dimensional potential where the Fourier grid method breaks down.
AB - We propose a method for solving the time-independent Schrödinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice, we solve a longstanding problem of convergence of the vN method. This opens the door to tailoring quantum calculations to the underlying classical phase space structure while retaining the accuracy of the Fourier grid basis. The method has the potential to provide enormous numerical savings as the dimensionality increases. In the classical limit, the method reaches the remarkable efficiency of one basis function per one eigenstate. We illustrate the method for a challenging two-dimensional potential where the Fourier grid method breaks down.
UR - http://www.scopus.com/inward/record.url?scp=84865257620&partnerID=8YFLogxK
U2 - https://doi.org/10.1103/PhysRevLett.109.070402
DO - https://doi.org/10.1103/PhysRevLett.109.070402
M3 - مقالة
SN - 0031-9007
VL - 109
JO - Physical review letters
JF - Physical review letters
IS - 7
M1 - 070402
ER -