一种新的相互作用N体波函数的检验
A Test of a New Interacting N-Body Wave Function
摘要：
解决一般的相互作用量子N体问题所需的资源与N成指数关系，使得当N很大时解决这个问题非常困难。在以前的一系列论文中，我们发展了一种方法，一个完全相互作用的波函数与一般的两体相互作用，驯服的N-标度通过开发一个扰动系列，是一个逐阶不变的点群同构的S_N。群论和图形技术，然后用来解决的波函数准确和分析在每一个订单。最近，这种形式已被用来获得一阶，完全相互作用的波函数的系统的谐波约束玻色子谐波相互作用。在本文中，我们报告的第一个应用程序的N体波函数的N个完全相互作用玻色子在三维系统。我们确定了一个有限系统的谐波相互作用玻色子的密度分布。选择这种简单的相互作用是没有必要的，甚至对我们的方法有利，但是这种选择允许我们的精确结果直接比较，通过一阶与在一个独立的解决方案中获得的精确结果。我们的密度分布，通过一阶在三维空间中是无法区分的一阶精确结果独立获得，并显示出强收敛到所有订单的精确结果。
英文摘要：
The resources required to solve the general interacting quantum N-body problem scale exponentially with N, making the solution of this problem very difficult when N is large. In a previous series of papers we develop an approach for a fully-interacting wave function with a general two-body interaction which tames the N-scaling by developing a perturbation series that is order-by-order invariant under a point group isomorphic with S_N . Group theory and graphical techniques are then used to solve for the wave function exactly and analytically at each order. Recently this formalism has been used to obtain the first-order, fully-interacting wave function for a system of harmonically-confined bosons interacting harmonically. In this paper, we report the first application of this N-body wave function to a system of N fully-interacting bosons in three dimensions. We determine the density profile for a confined system of harmonically-interacting bosons. Choosing this simple interaction is not necessary or even advantageous for our method, however this choice allows a direct comparison of our exact results through first order with exact results obtained in an independent solution. Our density profile through first-order in three dimensions is indistinguishable from the first-order exact result obtained independently and shows strong convergence to the exact result to all orders.
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