Department of Chemistry, University of Houston, Houston, Texas 77204, USA.
J Phys Chem A. 2009 Dec 31;113(52):15276-80. doi: 10.1021/jp9058017.
We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that Monte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schrodinger equation. Since the ground state of each partner potential is nodeless, we avoid any "node" problem typically associated with the Monte Carlo technique. Although we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions.
我们在此提出了一种在量子蒙特卡罗方案背景下确定激发能的超对称（SUSY）方法。通过利用 SUSY 量子力学产生一系列等谱哈密顿量这一事实，我们表明，在 SUSY 伴子中的蒙特卡罗基态计算可被用于精确重构任意薛定谔方程的谱和态。由于每个伴子势的基态是无节点的，我们避免了与蒙特卡罗技术相关的通常的“节点”问题。虽然我们提供了一个使用该方法来确定双势阱中的隧道态的例子，但该方法适用于任何 1D 势问题。我们最后讨论了向更高维度的扩展。
