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 本文已被：浏览 1062次   下载 1319次 码上扫一扫！ 分享到： 微信 更多 字体:加大+|默认|缩小- Algebraic Recursion Formulas for Perturbation Calculationof Energy Levels and Wave Functions in Potential Wells She Shouxian,Wu Liu,Wang Jian,Zhang Sijiong
 Author Name Affiliation She Shouxian Department ofPhysics, Northern Jiaotong University, Beijing　100044 Wu Liu Department ofPhysics, Northern Jiaotong University, Beijing　100044 Wang Jian Department ofPhysics, Northern Jiaotong University, Beijing　100044 Zhang Sijiong Department ofPhysics, Northern Jiaotong University, Beijing　100044
Abstract:
Using hypervirial theorem (HVT) and Hellmann-Feynman theorem (HFT), perturbation calculation of successive order approximate values of energy levels in a potential well with power series expansion of the potential energy are processed. Algebraic recursion formulas for calculating energy levels are deduced. We use the exact energy levels for parabolic potential well (one dimensional harmonic oscillator) as zero order approximation, and derive algebraic formulas for successive order approximate energy levels for given potential energy function. The corresponding wave functions can then be written as polynomials in which coefficients are expressed in terms of the energy levels and coefficients in the power series of potential energy. In this way, tedious and cumbersome perturbation calculations in Rayleigh-Schr dinger perturbation method are avoided. Thus the present method is simple, efficient and time saving. Typical examples are illustrated with the algebraic formulas, including: energy levels for Gaussian potential well; for modified P schel-Teller well; potential wells for anharmonic oscillators; Morse potential for vibrational energy levels of diatomic molecules and modified Morse potential for vibrational-rotational energy levels. Formulas for calculation of wave functions corresponding to calculated energy levels are given for anharmonic oscillators and for symmetric potential energy functions. The present method can be extended to two or three dimensional potential well, and can also be used in other mathematically analogous eigenvalue problem
Key words:  Energy levels, Wave function, Perturbation theory, Algebraic recursion formulas
FundProject:北方交通大学科技论文基金资助.

DOI：10.1088/1674-0068/14/4/403-413