A modified Euler–Maclaurin formula in 1D and 2D with applications in statistical physics
A modified Euler–Maclaurin formula in 1D and 2D with applications in statistical physics
复制标题
修改后的一维和二维欧拉-麦克劳林公式及其在统计物理中的应用
DOI：
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发表时间：
2020
影响因子：
3.1
通讯作者：
Yunpeng Liu
中科院分区：
文献类型：
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作者：
Jihong Guo;Yunpeng Liu
通过将周期Bernoulli多项式展开为Fourier级数并取截数，将Euler-Maclaurin求和公式推广为一种修正形式，其中包括Euler-Maclaurin求和公式和Poisson求和公式.利用修改后的公式，得到了一种可能的数值求和方法，并且可以控制余项。修正后的公式也从一维推广到二维。通过误差估计，得到了一维和二维方势阱中经典粒子配分函数以及量子旋转体配分函数的近似表达式。
The Euler–Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler–Maclaurin summation formula and the Poisson summation formula as special cases. By making use of the modified formula, a possible numerical summation method is obtained and the remainder can be controlled. The modified formula is also generalized from one dimension to two dimensions. Approximate expressions of partition functions of a classical particle in square well in 1D and 2D and that of a quantum rotator are obtained with error estimation.