解离的双原子Hartree模型
The diatomic Hartree model at dissociation
摘要：
本文研究了两个自旋电子的Hartree模型，它们分别处于二维和三维库仑相互作用空间中，并受到两个电荷为+1的原子核所诱导的势的作用。在核移动远离对方的限制，我们表明，平均场哈密顿量的两个最低本征函数是渐近给出的一个偶数，分别奇数，叠加的极小与相应的Hartree一个核模型。然后，我们给出了上界和下界的指数小的差距之间的前两个本征值，由于（非线性）量子隧穿。
英文摘要：
We study the Hartree model for two electrons with spin, living in the two-dimensional or three-dimensional space with Coulomb interactions and submitted to the potential induced by two nuclei of charge +1. In the limit where the nuclei move away from each other, we show that the two lowest eigenfunctions of the mean-field hamiltonian are asymptotically given by an even, respectively odd, superposition of the minimizer associated with the corresponding Hartree one nucleus model. We then give upper and lower bounds on the exponentially small gap between the first two eigenvalues, due to (nonlinear) quantum tunneling.
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