论文标题
各向异性偶极 - 偶极相互作用的schrödinger方程的溶液加上各向同性范德华相互作用
Solutions of the Schrödinger equation for anisotropic dipole-dipole interaction plus isotropic van der Waals interaction
论文作者
论文摘要
通过概括Bo Gao的方法[物理学。 Rev. A 58，1728（1998）]用于求解Schrödinger方程的各向同性范德华（VDW）的潜在，具有多尺度各向异性长距离交互的系统，我们得出了Schrödinger方程的解决方案，用于schrödinger方程的Anisotropic Dipole-Dipole-Dipole-Dipole-dipole-dipole-dipole-dipiC iSOTROPIC I. $ {c_d（1-3 \ cos^2θ）}/{r^3} - {c_6}/{r^6} $，该$将以角动量$ l \ leq l \ leq l _ {\ rm cut} $投影给子空间，带有$ l _ {\ rm cut cut} $ cut cut} $ cut cut cut。这里$θ$是坐标$ \ boldsymbol {r} $和$ r = | \ boldsymbol {r} | $的极性角度。获得了这些解决方案的渐近行为，以$ r \ rightarrow 0 $和$ r \ rightarrow \ infty $。这些结果可用于研究静态电场中超冷极分子之间的碰撞和化学反应。我们得出解决方案的方法可以应用于具有一般远程$ \ sum_ {λ= 2}^{λ_ {λ_ {\ rm max}} {v_λ（θ，φ）}/{r^λ} $的$ \ $ \ byl boldsymbol {r Boldsymbol {r bold boll {r bold boll {rmbol {rmbol {rmbol {rmbol {rmbol {rmbol {rmbol {rmbol {rmbol {rmbol {r，分子 - 分子相互作用。
By generalizing Bo Gao's approach [Phys. Rev. A 58, 1728 (1998)] for solving the Schrödinger equation for an isotropic van der Waals (vdW) potential to the systems with a multi-scale anisotropic long-range interaction, we derive the solutions for the Schrödinger equation for an anisotropic dipole-dipole interaction plus an isotropic attractive vdW potential, i.e., ${C_d(1-3\cos^2θ)}/{r^3}-{C_6}/{r^6}$, which is projected to the subspace with angular momentum $l\leq l_{\rm cut}$, with $l_{\rm cut}$ being an arbitrary angular-momentum cutoff. Here $θ$ is the polar angle of the coordinate $\boldsymbol{r}$ and $r=|\boldsymbol{r}|$. The asymptotic behaviors of these solutions for $r\rightarrow 0$ and $r\rightarrow \infty$ are obtained. These results can be used in the research of collisions and chemical reactions between ultra-cold polar molecules in a static electric field. Our approach to derive the solutions can be applied to the systems with a general long-range potential $\sum_{λ= 2}^{λ_{\rm max}} {V_λ(θ,φ)}/{r^λ}$, with $φ$ being the azimuthal angle of $\boldsymbol{r}$, and thus can be used in various problems on molecule-molecule interaction.
