将波函数近似为斯莱特行列式的无约束和
Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants
AI总结：
提出一种无约束的斯莱特行列式求和方法来近似多粒子薛定谔方程的波函数，通过积分公式、格林函数迭代和分离表示拟合，构建并求解由反对称内积导出的矩阵积分系统，计算复杂度与现有方法相当。
摘要：
多粒子薛定谔方程的波函数是多个变量的函数，并满足反对称条件，因此将其近似为斯莱特行列式的和是自然的。许多现有方法都这样做，但它们对行列式施加了额外的结构约束，例如轨道之间的正交性或激发模式。我们提出了一种没有任何此类约束的方法，希望通过这种方法获得更高效的展开，并洞察波函数的内在结构。我们使用问题的积分公式、格林函数迭代以及基于分离表示计算范式的拟合过程。核心过程是构建和求解一个由涉及势算子的反对称内积导出的矩阵积分系统。我们展示了如何构建和求解该系统，其计算复杂度与现有方法相当。
英文摘要：
The wavefunction for the multiparticle Schrödinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions, and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.
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