A new non-perturbative approach in quantum mechanics for time-independent Schr?dinger equations  

作　　者：ShiJun Liao 

机构地区：[1]Center of Advanced Computing,School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China [2]School of Physics and Astronomy,Shanghai Jiao Tong University,Shanghai 200240,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2020年第3期70-81,共12页中国科学：物理学、力学、天文学（英文版）

基　　金：National Natural Science Foundation of China(Grant Nos.11432009,and 91752104)。

摘　　要：A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum mechanics.It is based on the homotopy analysis method(HAM)that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many fields.Unlike perturbative methods,this HAM-based approach has nothing to do with small/large physical parameters.Besides,convergent series solution can be obtained even if the disturbance is far from the known status.A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative approach.This HAM-based approach could provide us rigorous theoretical results in quantum mechanics,which can be directly compared with experimental data.Obviously,this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories.A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum mechanics. It is based on the homotopy analysis method(HAM) that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many fields. Unlike perturbative methods, this HAM-based approach has nothing to do with small/large physical parameters. Besides, convergent series solution can be obtained even if the disturbance is far from the known status. A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative approach. This HAM-based approach could provide us rigorous theoretical results in quantum mechanics, which can be directly compared with experimental data. Obviously, this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories.

关 键 词：NON-PERTURBATIVE series HOMOTOPY analysis method quantum MECHANICS 

分 类 号：O413.1[理学—理论物理]