二维氢原子能级的精细结构  

THE FINE STRUCTURE OF ENERGY LEVELS IN A 2-D HYDROGEN ATOM

作　　者：柯善哲[1] 

机构地区：[1]南京大学物理系

出　　处：《南京大学学报（自然科学版）》1995年第1期25-32,共8页Journal of Nanjing University（Natural Science）

摘　　要：对于二维氢原子，其狄拉克方程中不出现ｘ３，对于因ｘ３隐退而简化了的狄拉克代数可取二维表示，于是严格求得能级的精加结构：Ｅ＝μ／，１＋Ｚ２ａ２／（ｖ＋ｎｐ）２将二维和三维氢原子的能级作比较，可见维度降低导致相应能级降低而能级间隔增大．The fine structure of energy levels for a 2- D hydrogen atom has been obtained by solving the corresponding 2-D Dirac equation exactly. Owing to the low dimensionality, a3 does not appear in the equation. The 2-D representation has been taken for the simplified Dirac algebra: al = σ1= ,a2=σ2=β=σ3 The polar coordinates have been taken for the 2- Dx, then the Hamitonian and the total angular momentum for a 2- Dhydrogen atom are represenated by Because [H,J3] = 0, the eigenfunctions of J3 are simultaneously also eigenfunctions of H. The eigenfuctions of J3 correspond to eigenvalue Dirac equation HΨ(x)=EΨ(x) isWhere g(p), and f(p) are functions satisfying following equations and boundary conditions When p→0 or ∞, f(p)→0 and g(p)→0 By comparing energy levels of a 2-D hydrogen atom with those of a 3-Dhydrogen atom, it may be seen that decrease in energy levels is caused by reduction of dimensionality, but spacing between energy levels is increased.

关 键 词：二维 氢原子 狄拉克方程 能级 精细结构 

分 类 号：O562.1[理学—原子与分子物理]