<![CDATA[<address id="ibjk4"></address>]]>
|
|
|
|
| <![CDATA[<address id="ibjk4"></address>]]><![CDATA[<dfn id="ibjk4"></dfn>]]><![CDATA[<object id="ibjk4"><td id="ibjk4"></td></object>]]>
| | | |
| |
|
|
|
|
<![CDATA[<address id="ibjk4"></address>]]>
|
|
|
|
| <![CDATA[<address id="ibjk4"></address>]]><![CDATA[<dfn id="ibjk4"></dfn>]]><![CDATA[<object id="ibjk4"><td id="ibjk4"></td></object>]]>
| | | |
| |
|
|
|
|
%7D%2B%7B%5Cfrac%7B%7B%7B%7Be%7D%7D%5E%7B%7B2%7D%7D%7D%7D%7B%7B%7Br%7D_%7B%7B%7B12%7D%7D%7D%7D%7D%7D%3D%7B%5Chat%7B%7B%7BH%7D%7D%7D%7D_%7B%7B0%7D%7D%2B%7B%5Cfrac%7B%7B%7B%7Be%7D%7D%5E%7B%7B2%7D%7D%7D%7D%7B%7B%7Br%7D_%7B%7B%7B12%7D%7D%7D%7D%7D%7D "hat{H}=sum_{\alpha=1}^2(\frac{1}{2\mu}hat{p}_\alpha^2-\frac{2e^2}{r_\alpha})+\frac{e^2}{r_{12}}=hat{H}_0+\frac{e^2}{r_{12}}")
的本征值問題。不計(jì)與自旋有關(guān)的能量，軌道運(yùn)動(dòng)和自旋運(yùn)動(dòng)是分離變量的。每個(gè)獨(dú)立單電子的軌道波函數(shù)都是Z=2的類氫離子的波函數(shù)ψnlm，相應(yīng)的能量為
。%7D%7D%7D%7D%3D%5Cpsi_%7B%7B%7B100%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B1%7D%7D%5Cright)%7D%5Cpsi_%7B%7B%7B100%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B2%7D%7D%5Cright)%7D%5Cchi_%7B%7B%7B00%7D%7D%7D%5C%5C%7B%5Cpsi_%7B%7B%7B1%7D%7Bn%7D%7Bs%7D%7Bm%7D_%7B%7Bs%7D%7D%7D%7D%5E%7B%7B%7B%5Cleft(%7B0%7D%5Cright)%7D%7D%7D%7D%3D%7B%5Cfrac%7B%7B%7B1%7D%7D%7D%7B%7B%5Csqrt%7B%7B%7B2%7D%7D%7D%7D%7D%7D%7B%5Cleft%5B%5Cpsi_%7B%7B%7B100%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B1%7D%7D%5Cright)%7D%5Cpsi_%7B%7B%7Bn%7D%7Bl%7D%7Bm%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B2%7D%7D%5Cright)%7D%5Cpm%5Cpsi_%7B%7B%7Bn%7D%7Bl%7D%7Bm%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B1%7D%7D%5Cright)%7D%5Cpsi_%7B%7B%7B100%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B2%7D%7D%5Cright)%7D%5Cright%5D%7D%7B%5Cleft.%5Cmatrix%7B%5Cchi_%7B%7B%7B00%7D%7D%7D%5C%5C%5Cchi_%7B%7B%7B1%7D%7Bm%7D_%7B%7Bs%7D%7D%7D%7D%7D%5Cright.%7D%7D%5Cright%5Crbrace%7D "{:[\psi_g^{(0)}=\psi_{100}(bb{x}_1)\psi_{100}(bb{x}_2)\chi_{00}],[\psi_{1nsm_s}^{(0)}=\frac{1}{sqrt{2}}[\psi_{100}(bb{x}_1)\psi_{nlm}(bb{x}_2)\pm\psi_{nlm}(bb{x}_1)\psi_{100}(bb{x}_2)]{:[\chi_{00}],[\chi_{1m_s}]:}]}")
（1） %7D%5Cxi_%7B%7B-%7D%7D%7B%5Cleft(%7B2%7D%5Cright)%7D-%5Cxi_%7B%7B-%7D%7D%7B%5Cleft(%7B1%7D%5Cright)%7D%5Cxi_%7B%7B%2B%7D%7D%7B%5Cleft(%7B2%7D%5Cright)%7D%5Cright%5D%7D "\chi_{00}=\frac{1}{sqrt{2}}[\xi_{+}(1)\xi_{-}(2)-\xi_{-}(1)\xi_{+}(2)]")
%7D%5Cxi_%7B%7B-%7D%7D%7B%5Cleft(%7B2%7D%5Cright)%7D%2B%5Cxi_%7B%7B-%7D%7D%7B%5Cleft(%7B1%7D%5Cright)%7D%5Cxi_%7B%7B%2B%7D%7D%7B%5Cleft(%7B2%7D%5Cright)%7D%5Cright%5D%7D "\chi_{10}=\frac{1}{sqrt{2}}[\xi_{+}(1)\xi_{-}(2)+\xi_{-}(1)\xi_{+}(2)]")
可作微擾處理。由微擾論求得能量： 
%7D%5Cright%7C%7D%7D%5E%7B%7B2%7D%7D%7B%7B%5Cleft%7C%5Cpsi_%7B%7B%7B100%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B2%7D%7D%5Cright)%7D%5Cright%7C%7D%7D%5E%7B%7B2%7D%7D%7D%7D%7B%7B%7B%5Cleft%7C%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B1%7D%7D-%7B%5Cmathbf%7B%7B%7Bx%7D_%7B%7B2%7D%7D%7D%7D%7D%5Cright%7C%7D%7D%7D%7D "J_g=e^2intint d^3x_1d^3x_2\frac{|\psi_{100}(bb{x}_1)|^2|\psi_{100}(bb{x}_2)|^2}{|bb{x}_1-bb{x_2}|}")
，和實(shí)驗(yàn)值
基本一致。采用變分法計(jì)算，理論值和實(shí)驗(yàn)值符合得很好； %7D%2B%7BJ%7D%5Cpm%7BK%7D "E_{nl}=\frac{-4e^2}{2a_0}(1+\frac{1}{n^2})+J\pmK")
（2） %7D%5Cright%7C%7D%7D%5E%7B%7B2%7D%7D%7B%7B%5Cleft%7C%5Cpsi_%7B%7B%7Bn%7D%7Bl%7D%7Bm%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B2%7D%7D%5Cright)%7D%5Cright%7C%7D%7D%5E%7B%7B2%7D%7D%7D%7D%7B%7B%7B%5Cleft%7C%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B1%7D%7D-%7B%5Cmathbf%7B%7B%7Bx%7D_%7B%7B2%7D%7D%7D%7D%7D%5Cright%7C%7D%7D%7D%7D "J=e^2intint d^3x_1d^3x_2\frac{|\psi_{100}(bb{x}_1)|^2|\psi_{nlm}(bb{x}_2)|^2}{|bb{x}_1-bb{x_2}|}")
%7D%5Cpsi_%7B%7B%7Bn%7D%7Bl%7D%7Bm%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B1%7D%7D%5Cright)%7D%7B%5Cpsi_%7B%7B%7Bn%7D%7Bl%7D%7Bm%7D%7D%7D%5E%7B%5Cast%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B2%7D%7D%5Cright)%7D%5Cpsi_%7B%7B%7B100%7D%7D%7D%7B%5Cleft(%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B2%7D%7D%5Cright)%7D%7D%7D%7B%7B%7B%5Cleft%7C%7B%5Cmathbf%7B%7B%7Bx%7D%7D%7D%7D_%7B%7B1%7D%7D-%7B%5Cmathbf%7B%7B%7Bx%7D_%7B%7B2%7D%7D%7D%7D%7D%5Cright%7C%7D%7D%7D%7D "K=e^2intint d^3x_1d^3x_2\frac{\psi_{100}^\**(bb{x}_1)\psi_{nlm}(bb{x}_1)\psi_{nlm}^\**(bb{x}_2)\psi_{100}(bb{x}_2)}{|bb{x}_1-bb{x_2}|}")
