General exact solutions of the second-order homogeneous algebraic differential equations

2014 ◽  
Vol 63 (2) ◽  
pp. 244-263 ◽  
Author(s):  
Qingxiang Xu ◽  
Chuanning Song ◽  
Xiaofang Liu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Second Order ◽  
Algebraic Differential Equations

EXACT SOLUTIONS OF THE DIRAC EQUATION WITH A COULOMB PLUS SCALAR POTENTIAL IN 2 + 1 DIMENSIONS

2002 ◽  
Vol 11 (06) ◽  
pp. 483-489 ◽  
Author(s):  
SHI-HAI DONG ◽  
XIAO-YAN GU ◽  
ZHONG-QI MA ◽  
SHISHAN DONG
Keyword(s):  
Dirac Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Coulomb Potential ◽  
Scalar Potential ◽  
Second Order ◽  
First Order ◽  
Second Order Differential Equations

The exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones. The eigenvalues are studied in some detail.

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