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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振动频率、基态能量和基态结合能随库仑束缚势、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、基态能量和基态结合能随库仑束缚势的增加而增大，基态能量和基态结合能随电子一声子耦合强度的增加而增加。当e’〉1时，振动频率、基态能量和基态结合能随椭球的纵横比的增加而增加；e＇〈1时，随纵横比的减少，振动频率、基态能量和基态结合能都增大；当e’=1时，振动频率取极小值，基态能量和基态结合能也取较小的稳定值。
英文摘要：
The Hamihonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation which can transform the boundary into a spherical one. The relations of the vibrational frequency, the ground state energy and the ground state binding energy of weak- coupling impurity bound polaron in a quantum rod with the Coulomb bound potential, the elec- tron-phonon coupling strength and the aspect ratio of the ellipsoid are studied by using the linear combination operator and the unitary transformation methods. Numerical calculations are per- formed and the results show that they will increase with increasing Coulomb bound potential. The ground state energy and the ground state binding energy are increasing functions of the elec- tron-phonon coupling strength. The vibrational frequency, the ground state energy and the ground state binding energy are increasing functions of the aspect ratio of the ellipsoid when e＇〉 1, whereas they are decreasing functions of one when e＇〈1. Whene＇=1, the vibrational frequency is a minimum value and the ground state energy and the ground state binding energy are a less steady value.
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