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中文摘要：
给出了具有椭球边界量子棒经过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弱耦合杂质束缚极化子的性质．导出了量子棒中弱耦合杂质束缚极化子的振动频率随库仑束缚势和椭球的纵横比的变化关系以及声子平均数随电子一声子耦合强度和椭球的纵横比的变化关系．数值计算结果表明：振动频率随库仑束缚势的增加而增加，当e′〉1时，振动频率随椭球的纵横比的增加而增加．e′〈1时，随着椭球的纵横比的减少，振动频率增大．当e′=1时，振动频率取极小值．声子平均数随电子一声子耦合强度的增加而增加，随着椭球的纵横比的减少而增大．
英文摘要：
The Hamihonian of a quantum rods with an ellipsoidal boundary is given after a coordinate transformation which can transform the boundary into a spherical one. The properties of the weak -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 relations of the vibrational frequency of weak-coupling impurity bound polaron in a quantum rod with the Coulomb bound potential and the aspect ratio of the ellipsoid and the mean number of phonons with the electron-phonon coupling strength and the aspect ratio of the ellipsoid were derived. Numerical calculations are performed and the results show that the vibrational frequency will increase with increasing the Coulomb bound potential. The vibrational frequency is increasing functions of the aspect ratio of the ellipsoid when e′〉1, whereas it is decreasing functions of one when e′〈1. Whene′=1, the vibrational frequency have a minimum value. The mean number of phonons is increasing functions of the electron-phonon coupling strength whereas it is decreasing functions of the aspect ratio of the ellipsoid.
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