中文摘要：

给出了具有椭球边界量子棒经坐标变换成球形边界的哈密顿量。采用线性组合算符和幺正变换的方法研究了在非均匀抛物限制势下量子棒中强耦合杂质束缚极化子的性质。导出了量子棒中强耦合杂质束缚极化子的振动频率和声子平均数随库仑束缚势、电子-声子耦合强度、椭球的纵横比和量子棒的横向和纵向有效受限长度的变化关系。数值计算结果表明：振动频率和声子平均数随电子-声子耦合强度和库仑束缚势的增强而增加,随量子棒的横向和纵向有效受限长度和椭球的纵横比的减小而增大。表现出量子棒的奇特的量子尺寸限制效应。

英文摘要：

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation which can transform the ellipsoidal boundary into spherical one.The properties of the strong-coupling impurity bound polaron in a quantum rod in a three-dimensional anisotropic harmonic potential are studied by using the linear combination operator and the unitary transformation methods.The relationships among the vibrational frequency,the mean number of phonons of strong-coupling impurity bound polaron in a quantum rod and the Coulomb bound potential,the electron-phonon coupling strength,the aspect ratio of the ellipsoid and the transverse and the longitudinal effective confinement length of quantum rods were derived.Numerical calculations are performed and the results show that the vibrational frequency and the mean number of phonons increase the electron-phonon coupling strength and the Coulomb bound potential,decrease with the transverse and the longitudinal effective confinement length of quantum rods and the aspect ratio of the ellipsoid.These can be attributed to the interesting quantum size confining effects.