超对称性识别分子斯塔克态，其本征性质可以解析地获得
Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically
摘要：
利用超对称（SUSY）量子力学找到了一个条件，在该条件下，极性和可极化闭壳层双原子分子在共线静电场和非共振辐射场作用下的Stark效应问题成为精确可解的.条件$Δω= \frac{ω^2}{4 (m+1)^2}$将表征分子与相应场的永久和诱导偶极相互作用的强度的无量纲参数$ω$和$Δω$的值连接起来。得到了$|\tilde{J}=m,m;ω,Δω>$族“拉伸”态的精确解。组合场问题的无场极限和强场极限表现出超对称性和形状不变性，这确实是它们解析可解的原因。利用$|\tilde{J}=m,m;ω,Δω>$波函数的解析形式，我们得到了空间固定电偶极矩、排列余弦、角动量平方的期望值的简单公式，并导出了将上述期望值组合成本征能公式的“求和规则”。强取向和对齐状态的特性的解析表达式提供了在实验室中创建这种状态所需的相互作用参数的值的直接访问。
英文摘要：
We made use of supersymmetric (SUSY) quantum mechanics to find a condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subject to collinear electrostatic and nonresonant radiative fields becomes exactly solvable. The condition, $Δω= \frac{ω^2}{4 (m+1)^2}$, connects values of the dimensionless parameters $ω$ and $Δω$ that characterize the strengths of the permanent and induced dipole interactions of the molecule with the respective fields. The exact solutions are obtained for the $|\tilde{J}=m,m;ω,Δω>$ family of "stretched" states. The field-free and strong-field limits of the combined-fields problem were found to exhibit supersymmetry and shape-invariance, which is indeed the reason why they are analytically solvable. By making use of the analytic form of the $|\tilde{J}=m,m;ω,Δω>$ wavefunctions, we obtained simple formulae for the expectation values of the space-fixed electric dipole moment, the alignment cosine, the angular momentum squared, and derived a "sum rule" which combines the above expectation values into a formula for the eigenenergy. The analytic expressions for the characteristics of the strongly oriented and aligned states provide a direct access to the values of the interaction parameters required for creating such states in the laboratory.
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