User:Fatka/sandbox From Wikipedia, the free encyclopedia More information Userpage, Projects & Interests ... Userpage User Talk Projects & Interests User Books Sandbox Resources Close Signature testing Fatka (talk contribs) Fatka (talk · contribs) Fatka (talk · contribs) -Fatka (talk · contribs) -- Fatka (talk · contribs) -- Fatka (talk · contribs) 01:26, 10 November 2008 (UTC) 01:26, 10 November 2008 (UTC) - Fatka (talk · contribs) 19:03, 10 November 2008 (UTC) - Fatka (talk · contribs) 06:38, 25 March 2009 (UTC) LaTeX testing ≢ {\displaystyle \not \equiv } ≡ ⇒ done using <math> \begin{align} bla bla & = bla bla & = bla bla \end{align} </math> H ^ = p ^ 1 2 2 m e + p ^ 2 2 2 m e − Z e 2 | r 1 | − Z e 2 | r 2 | + e 2 | r 1 − r 2 | = [ p ^ 1 2 2 m e − Z ~ e 2 | r 1 | + p ^ 2 2 2 m e − Z ~ e 2 | r 1 | − Z ~ e 2 | r 2 | ] + [ ( Z ~ − Z ) e 2 | r 1 | + ( Z ~ − Z ) e 2 | r 2 | ] + e 2 | r 1 − r 2 | {\displaystyle {\begin{aligned}{\hat {H}}&={\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {Ze^{2}}{|\mathbf {r_{1}} |}}-{\frac {Ze^{2}}{|\mathbf {r_{2}} |}}+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\&=\left[{\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{2}} |}}\right]+\left[{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{1}} |}}+{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{2}} |}}\right]+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\\end{aligned}}} <math> \begin{alignat}{2} bla bla & = bla bla & = bla bla \end{alignat} </math> H ^ = p ^ 1 2 2 m e + p ^ 2 2 2 m e − Z e 2 | r 1 | − Z e 2 | r 2 | + e 2 | r 1 − r 2 | = [ p ^ 1 2 2 m e − Z ~ e 2 | r 1 | + p ^ 2 2 2 m e − Z ~ e 2 | r 1 | − Z ~ e 2 | r 2 | ] + [ ( Z ~ − Z ) e 2 | r 1 | + ( Z ~ − Z ) e 2 | r 2 | ] + e 2 | r 1 − r 2 | {\displaystyle {\begin{alignedat}{2}{\hat {H}}&={\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {Ze^{2}}{|\mathbf {r_{1}} |}}-{\frac {Ze^{2}}{|\mathbf {r_{2}} |}}+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\&=\left[{\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{2}} |}}\right]+\left[{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{1}} |}}+{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{2}} |}}\right]+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\\end{alignedat}}} Related Articles
![{\displaystyle {\begin{aligned}{\hat {H}}&={\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {Ze^{2}}{|\mathbf {r_{1}} |}}-{\frac {Ze^{2}}{|\mathbf {r_{2}} |}}+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\&=\left[{\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{2}} |}}\right]+\left[{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{1}} |}}+{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{2}} |}}\right]+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\\end{aligned}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/567e05d7b8c6c23b057f4a0eb2123b062823e4e7)
![{\displaystyle {\begin{alignedat}{2}{\hat {H}}&={\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {Ze^{2}}{|\mathbf {r_{1}} |}}-{\frac {Ze^{2}}{|\mathbf {r_{2}} |}}+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\&=\left[{\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{2}} |}}\right]+\left[{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{1}} |}}+{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{2}} |}}\right]+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\\end{alignedat}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7f5d1011574ad3cdc81e9a10463f8f410f115e51)
![{\displaystyle {\begin{aligned}{\hat {H}}&={\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {Ze^{2}}{|\mathbf {r_{1}} |}}-{\frac {Ze^{2}}{|\mathbf {r_{2}} |}}+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\&=\left[{\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{2}} |}}\right]+\left[{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{1}} |}}+{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{2}} |}}\right]+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\\end{aligned}}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/567e05d7b8c6c23b057f4a0eb2123b062823e4e7)
![{\displaystyle {\begin{alignedat}{2}{\hat {H}}&={\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {Ze^{2}}{|\mathbf {r_{1}} |}}-{\frac {Ze^{2}}{|\mathbf {r_{2}} |}}+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\&=\left[{\frac {\mathbf {{\hat {p}}_{1}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}+{\frac {\mathbf {{\hat {p}}_{2}} ^{2}}{2m_{e}}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{1}} |}}-{\frac {{\tilde {Z}}e^{2}}{|\mathbf {r_{2}} |}}\right]+\left[{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{1}} |}}+{\frac {({\tilde {Z}}-Z)e^{2}}{|\mathbf {r_{2}} |}}\right]+{\frac {e^{2}}{|\mathbf {r_{1}-r_{2}} |}}\\\end{alignedat}}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/7f5d1011574ad3cdc81e9a10463f8f410f115e51)