量子棒中强耦合磁极化子的振动频率

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强耦合磁极化子的性质。导出了量子棒中强耦合磁极化子的振动频率和声子平均数随磁场的回旋频率、电子-声子耦合强度、椭球的纵横比和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-声子耦合强度和磁场的回旋频率的增加而增加，随横向和纵向有效受限长度的减小而迅速增大。当 时，振动频率和声子平均数随椭球的纵横比的增加而增加。 时，随着椭球的纵横比的减少，振动频率和声子平均数都增大。当 时，振动频率和声子平均数取极小值。

Vibrational frequency of strong-coupling magnetopolaron in a quantum rods

The Hamiltonian 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 strong-coupling magnetopolaron in a quantum rods 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 and the mean number of phonons of strong-coupling magnetopolaron in a quantum rods with the cyclotron frequency of a magnetic field ，the electron-phonon coupling strength, the aspect ratio of the ellipsoid and the transverse and the longitudinal effective confinement length were derived. Numerical calculations are performed and the results show that the vibrational frequency and the mean number of phonons will increase with increasing the electron-phonon coupling strength and the cyclotron frequency of a magnetic field and increase rapidly with decreasing transverse and the longitudinal effective confinement length. The vibrational frequency and the mean number of phonons are increasing functions of theaspect ratio of the ellipsoid when , whereas they are decreasing functions of one when .When , the vibrational frequency and the mean number of phonons are a minimum value.