利用自洽平均值近似方法处理二维非线性谐振子问题  

Two-dimensional Nonlinear Oscillator Problem Dealing with Average Self-consistent Field Approximation Method

作　　者：蔡德欢[1] 刘兰兰[1] 程荣龙[1] 许永红[1] 王晴晴[1] 宫昊[1] 葛立新[1] 

机构地区：[1]蚌埠学院数学与物理系,安徽蚌埠233030

出　　处：《蚌埠学院学报》2015年第5期30-33,38,共5页Journal of Bengbu University

基　　金：安徽省高校省级自然科学研究项目(KJ2014A151);蚌埠学院自然科学研究项目(2015ZR16)

摘　　要：利用自洽平均值近似方法分别求解哈密顿量含有不同微扰项的二维非线性谐振子系统的能量本征值和波函数,并与微扰理论所得结果进行比较。结果表明,自洽平均值近似方法可以有效地降低高次微扰项的幂次,简化计算过程,且可以给出非线性谐振子任意本征态下的能量本征值。The two-dimensional nonlinear oscillator energy eigenvalue and eigenstate whose Hamihonian contains different perturbation terms were obtained by using the average self-consistent approximation method respectively. It showed that compared with the results obtained by the perturbation theory, the calculation by using the self-consistent approximation can reduce the power of and it is simpler than the perturbation method in treating these models. The higher order perturbation term self-consistent approximation method can also give the energy eigenvalue of the arbitrary eigenstate.

关 键 词：自洽平均值近似方法 非线性谐振子 微扰理论 

分 类 号：O413.1[理学—理论物理]