A general analytic approach,namely the homotopy analysis method(HAM),is applied to solve the time independent Schrodinger equations.Unlike perturbation method,the HAM-based approach does not depend on any small physic...A general analytic approach,namely the homotopy analysis method(HAM),is applied to solve the time independent Schrodinger equations.Unlike perturbation method,the HAM-based approach does not depend on any small physical parameters,corresponding to small disturbances.Especially,it provides a convenient way to gain the convergent series solution of quantum mechanics.This study illustrates the advantages of this HAM-based approach over the traditional perturbative approach,and its general validity for the Schrodinger equations.Note that perturbation methods are widely used in quantum mechanics,but perturbation results are hardly convergent.This study suggests that the HAM might provide us a new,powerful alternative to gain convergent series solution for some complicated problems in quantum mechanics,including many-body problems,which can be directly compared with the experiment data to improve the accuracy of the experimental findings and/or physical theories.展开更多
基金partly supported by the National Natural Science Foundation of China(No.11432009)
文摘A general analytic approach,namely the homotopy analysis method(HAM),is applied to solve the time independent Schrodinger equations.Unlike perturbation method,the HAM-based approach does not depend on any small physical parameters,corresponding to small disturbances.Especially,it provides a convenient way to gain the convergent series solution of quantum mechanics.This study illustrates the advantages of this HAM-based approach over the traditional perturbative approach,and its general validity for the Schrodinger equations.Note that perturbation methods are widely used in quantum mechanics,but perturbation results are hardly convergent.This study suggests that the HAM might provide us a new,powerful alternative to gain convergent series solution for some complicated problems in quantum mechanics,including many-body problems,which can be directly compared with the experiment data to improve the accuracy of the experimental findings and/or physical theories.
