论文标题
关于Born-oppenheimer近似中的四体问题
On the four-body problem in the Born-Oppenheimer approximation
论文作者
论文摘要
$ \ mathbb {r}^d $中的四个粒子的量子问题（$ d \ geq 3 $），带有任意质量$ m_1，m_2，m_3 $和$ m_4 $，通过谐波振荡器电位进行交互。该模型允许对Born-Oppenheimer近似的精确溶解度和批判性分析。该研究仅限于基态水平。我们特别注意两个同样重的质量$ m_1 = m_2 = m $和两个光粒子$ m_3 = m_4 = m $。结果表明，Puiseux系列的前两个术语的总和在无量纲参数$σ= \ frac {m} {m} {m} $的幂中，是Wave Wave函数的确切相位$φ$的$ψ_0= e^{ - φ} $的$ c $ coccip conconce conconce conconce conconim conconiim conconiim youm conceim concemiim concemim concement。详细描述了$ H_2 $分子和化合物$ H_2O_2 $（过氧化氢）的物理相关的粗糙模型。对任意数量的粒子$ n $的概括（$ d $ d $ d $ d $ d \ geq n-1 $），也通过谐波振荡器电位进行了简要讨论。
The quantum problem of four particles in $\mathbb{R}^d$ ($d\geq 3$), with arbitrary masses $m_1,m_2,m_3$ and $m_4$, interacting through an harmonic oscillator potential is considered. This model allows exact solvability and a critical analysis of the Born-Oppenheimer approximation. The study is restricted to the ground state level. We pay special attention to the case of two equally heavy masses $m_1=m_2=M$ and two light particles $m_3=m_4=m$. It is shown that the sum of the first two terms of the Puiseux series, in powers of the dimensionless parameter $σ=\frac{m}{M}$, of the exact phase $Φ$ of the wave function $ψ_0=e^{-Φ}$ and the corresponding ground state energy $E_0$, coincide exactly with the values obtained in the Born-Oppenheimer approximation. A physically relevant rough model of the $H_2$ molecule and of the chemical compound $H_2O_2$ (Hydrogen peroxide) is described in detail. The generalization to an arbitrary number of particles $n$, with $d$ degrees of freedom ($d\geq n-1$), interacting through an harmonic oscillator potential is briefly discussed as well.
