High Order Perturbation Theory for a Generalized Central Field Perturbation of the Three‐Dimensional Harmonic Oscillator
High Order Perturbation Theory for a Generalized Central Field Perturbation of the Three‐Dimensional Harmonic Oscillator
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三维谐波振荡器广义中心场扰动的高阶微扰理论
DOI：
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发表时间：
1972
期刊：
影响因子：
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通讯作者：
L. B. Mendelsohn
中科院分区：
文献类型：
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作者：
A. Ehlenberger;L. B. Mendelsohn
提出了一种解决三维谐振子对任意阶扰动的一般偶阶扰动的方法。我们发现，使用迭代过程可以将 n 阶扰动波函数表示为 4n 项之和。这些 4n 项取决于所有低阶扰动波函数和能量校正，并且可以很容易地评估。研究还表明，如果将能量重新表示为 Pade 近似，则可以在大扰动下获得准确的结果。受四次项扰动的振荡器的九个最低能级被计算到十阶，结果与贝尔、戴维森和沃索普的二维混合谐波四次振荡器结果定性一致。
A method is presented to solve a general even‐order perturbation of the three‐dimensional harmonic oscillator to any order of perturbation. It is found that using an iterative process it is possible to express the nth order perturbation wavefunction as a sum of 4n terms. These 4n terms depend upon all the lower order perturbation wavefunctions and energy corrections, and may be easily evaluated. It is also shown that accurate results may be achieved for large perturbations if the energy is re‐expressed as a Pade approximant. The nine lowest levels of an oscillator perturbed by a quartic term are calculated to tenth order and the results agree qualitatively with the two dimensional mixed harmonic—quartic oscillator results of Bell, Davidson, and Warsop.