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Display information for equation id:math.1707.43 on revision:1707

* Page found: Zustände mit Bahn- und Spinvariablen (eq math.1707.43)

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TeX (original user input): 

\begin{align}
& \hat{H}\left| nlm{{m}_{s}} \right\rangle ={{H}_{0}}\left| nlm \right\rangle \left| {{m}_{s}} \right\rangle -\frac{\left| e \right|B}{2{{m}_{0}}}\left\{ \left( {{{\hat{L}}}_{3}}\left| nlm \right\rangle \right)\left| {{m}_{s}} \right\rangle +\hbar \left( {{{\hat{\bar{\sigma }}}}_{3}}\left| {{m}_{s}} \right\rangle \right)\left| nlm \right\rangle \right\} \\
& {{{\hat{L}}}_{3}}\left| nlm \right\rangle =\hbar m\left| nlm \right\rangle \\
& {{{\hat{\bar{\sigma }}}}_{3}}\left| {{m}_{s}} \right\rangle =2{{m}_{S}}\left| {{m}_{s}} \right\rangle \\
& {{H}_{0}}\left| nlm \right\rangle \left| {{m}_{s}} \right\rangle -\frac{\left| e \right|B}{2{{m}_{0}}}\left\{ \left( {{{\hat{L}}}_{3}}\left| nlm \right\rangle \right)\left| {{m}_{s}} \right\rangle +\hbar \left( {{{\hat{\bar{\sigma }}}}_{3}}\left| {{m}_{s}} \right\rangle \right)\left| nlm \right\rangle \right\}=\left[{{E}_{nl}}-\frac{\left| e \right|\hbar B}{2{{m}_{0}}}\left( m+2{{m}_{s}} \right) \right]\left| nlm{{m}_{s}} \right\rangle \\
\end{align}

TeX (checked): 

{\begin{aligned}&{\hat {H}}\left|nlm{{m}_{s}}\right\rangle ={{H}_{0}}\left|nlm\right\rangle \left|{{m}_{s}}\right\rangle -{\frac {\left|e\right|B}{2{{m}_{0}}}}\left\{\left({{\hat {L}}_{3}}\left|nlm\right\rangle \right)\left|{{m}_{s}}\right\rangle +\hbar \left({{\hat {\bar {\sigma }}}_{3}}\left|{{m}_{s}}\right\rangle \right)\left|nlm\right\rangle \right\}\\&{{\hat {L}}_{3}}\left|nlm\right\rangle =\hbar m\left|nlm\right\rangle \\&{{\hat {\bar {\sigma }}}_{3}}\left|{{m}_{s}}\right\rangle =2{{m}_{S}}\left|{{m}_{s}}\right\rangle \\&{{H}_{0}}\left|nlm\right\rangle \left|{{m}_{s}}\right\rangle -{\frac {\left|e\right|B}{2{{m}_{0}}}}\left\{\left({{\hat {L}}_{3}}\left|nlm\right\rangle \right)\left|{{m}_{s}}\right\rangle +\hbar \left({{\hat {\bar {\sigma }}}_{3}}\left|{{m}_{s}}\right\rangle \right)\left|nlm\right\rangle \right\}=\left[{{E}_{nl}}-{\frac {\left|e\right|\hbar B}{2{{m}_{0}}}}\left(m+2{{m}_{s}}\right)\right]\left|nlm{{m}_{s}}\right\rangle \\\end{aligned}}

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H^|nlmms⟩=H0|nlm⟩|ms⟩−|e|B2m0{(L^3|nlm⟩)|ms⟩+ℏ(σ¯^3|ms⟩)|nlm⟩}L^3|nlm⟩=ℏm|nlm⟩σ¯^3|ms⟩=2mS|ms⟩H0|nlm⟩|ms⟩−|e|B2m0{(L^3|nlm⟩)|ms⟩+ℏ(σ¯^3|ms⟩)|nlm⟩}=[Enl−|e|ℏB2m0(m+2ms)]|nlmms⟩
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Calculated based on the variables occurring on the entire Zustände mit Bahn- und Spinvariablen page

Identifiers

  • H^
  • n
  • l
  • m
  • ms
  • H0
  • n
  • l
  • m
  • ms
  • e
  • B
  • m0
  • L^3
  • n
  • l
  • m
  • ms
  • σ¯^3
  • ms
  • n
  • l
  • m
  • L^3
  • n
  • l
  • m
  • m
  • n
  • l
  • m
  • σ¯^3
  • ms
  • mS
  • ms
  • H0
  • n
  • l
  • m
  • ms
  • e
  • B
  • m0
  • L^3
  • n
  • l
  • m
  • ms
  • σ¯^3
  • ms
  • n
  • l
  • m
  • Enl
  • e
  • B
  • m0
  • m
  • ms
  • n
  • l
  • m
  • ms

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