数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (2): 274-.

• 论文 • 上一篇    

SOLVING SECOND ORDER DIFFERENTIAL EQUATIONS IN QUANTUM MECHANICS BY ORDER REDUCTION

 C. Ted Chen   

  1. Grace Semiconductor Manufacturing Corporation
    2nd Floor, 307 North Tun-Hwa Road, Taipei, Taiwan 10508, China
  • 出版日期:2003-04-07 发布日期:2003-04-07

SOLVING SECOND ORDER DIFFERENTIAL EQUATIONS IN QUANTUM MECHANICS BY ORDER REDUCTION

 C. Ted Chen   


  1. Grace Semiconductor Manufacturing Corporation
    2nd Floor, 307 North Tun-Hwa Road, Taipei, Taiwan 10508, China
  • Online:2003-04-07 Published:2003-04-07

摘要:

t Solving the famous Hermite, Legendre, Laguerre and Chebyshev equations
requires different techniques of unique character for each equation. By reducing these
differential equations of second order to a common solvable differential equation of first
order, a simple common solution is provided to cover all the existing standard solutions
of these named equations. It is easier than the method of generating functions and more
powerful than the Frobenius method of power series.

关键词: Second order differential equations, quantum mechanics, common solution

Abstract:

t Solving the famous Hermite, Legendre, Laguerre and Chebyshev equations
requires different techniques of unique character for each equation. By reducing these
differential equations of second order to a common solvable differential equation of first
order, a simple common solution is provided to cover all the existing standard solutions
of these named equations. It is easier than the method of generating functions and more
powerful than the Frobenius method of power series.

Key words: Second order differential equations, quantum mechanics, common solution

中图分类号: 

  • 34A