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么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极化子的振动频率λ、第一内部激发态能量E_l、激发能量AE和从激发态到基态跃迁谱线频率ω随椭球的纵横比e'、电子-声子耦合强度α和横向和纵向有效受限长度l_p和l_z的变化关系.数值计算结果表明:振动频率、第一内部激发态能量、激发能量和跃迁谱线频率随横向和纵向有效受限长度的减少而迅速增大.第一内部激发态能量随电子-声子耦合强度的增加而减少.振动频率随椭球纵横比的增加而减少.当e'>1时,激发能量和跃迁谱线频率随椭球纵横比的增加而增加.当e'<1时,随椭球纵横比的减少而增大.当e'＝1时,它们取极小值.
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