论文标题
1D中量子三体问题的结合状态的等几何分析
Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D
论文作者
论文摘要
在本文中，我们启动了量子三体问题的等几何分析（IGA），该问题众所周知难以解决。在IGA设置中，我们通过B-Spline基函数的线性组合表示波形，并将问题作为矩阵特征值问题解决。特征值给出了本征能的能量，而特征向量给出了导致本征态的b型系数的系数。基于数字或其他有限元方法分析的主要困难在于缺乏边界条件和精确度的自由度。对于有吸引力的相互作用的典型多体问题，有界面状态和散射状态，其中有限状态具有负特征值。我们专注于约束状态，并从分析两体问题开始。我们通过各种数值实验证明IGA提供了一种有希望的技术来解决三体问题。
In this paper, we initiate the study of isogeometric analysis (IGA) of a quantum three-body problem that has been well-known to be difficult to solve. In the IGA setting, we represent the wavefunctions by linear combinations of B-spline basis functions and solve the problem as a matrix eigenvalue problem. The eigenvalue gives the eigenstate energy while the eigenvector gives the coefficients of the B-splines that lead to the eigenstate. The major difficulty of isogeometric or other finite-element-method-based analyses lies in the lack of boundary conditions and a large number of degrees of freedom for accuracy. For a typical many-body problem with attractive interaction, there are bound and scattering states where bound states have negative eigenvalues. We focus on bound states and start with the analysis for a two-body problem. We demonstrate through various numerical experiments that IGA provides a promising technique to solve the three-body problem.
