求解与时间无关的薛定谔方程的相空间方法
Phase Space Approach to Solving the Time-independent Schrödinger Equation
摘要：
本文提出了一种基于相空间高斯的vN格点求解与时间无关的薛定谔方程的方法。通过将周期边界条件引入vN格[F. Dimler等人，New J.Phys.11，105052（2009）]，我们解决了vN方法的收敛性的长期问题。这为根据底层经典相空间结构定制量子计算，同时保持傅里叶网格基的准确性打开了大门。该方法有可能提供巨大的数值节省的维数增加。在经典极限下，该方法达到了每1个本征态1个基函数的显着效率。我们说明了一个具有挑战性的二维潜在的FGH方法分解的方法。
英文摘要：
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 [F. Dimler et al., New J. Phys. 11, 105052 (2009)] 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 1 basis function per 1 eigenstate. We illustrate the method for a challenging two-dimensional potential where the FGH method breaks down.
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