We present a classical and a quantum constant of motion used to study the behavior of an electron moving in the vicinity of a tridimensional charged nanostructure with electric dipole. It is the generalization of the bidimensional version studied in a previous work. The classical case is found by using two approaches: the Hamilton Jacobi equation and a Newtonian treatment. The quantum case is obtained by separating the Schrödinger equation in spherical coordinates. We use three quantum numbers to classify the states. The angular part is solved by using an expansion of spherical harmonics to get an eigenvalue equation for the new constant of motion. The solution shows that the probability density of the electron shifts toward the values where \(\theta <\frac {\pi }{2}\). The eigenvalue λ is near the value l(l + 1) of the angular momentum, but their difference grows if the electric dipole increases, so that the effect is small for a cluster like (GaAs)₃ but very important for fullerenes like RbC₆₀ and LiC₆₀. The radial part is solved using the shooting method and we find the ground state, and first and second excited states.

我们提出了一个经典的运动常数和一个量子常数，用于研究电子在带电偶极子的三维带电纳米结构附近移动的行为。它是先前工作中研究的二维版本的概括。通过使用两种方法可以找到经典情况：Hamilton Jacobi方程和牛顿处理。通过在球形坐标中分离Schrödinger方程获得量子情况。我们使用三个量子数对状态进行分类。通过使用球谐函数的展开来求解角部分，以获得新的运动常数的特征值方程。解表明，电子的概率密度朝着\（\ theta <\ frac {\ pi} {2} \）的值移动。特征值λ接近角动量的值l（l + 1），但是如果电偶极子增加，它们的差异就会增加，因此对于像（G a A s）₃的簇来说，影响很小，但是对于像R b的富勒烯来说却非常重要C ₆₀和L i C ₆₀。使用射击方法求解径向部分，我们找到基态以及第一和第二激发态。