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Display information for equation id:math.1750.17 on revision:1750

* Page found: Zeitunabhängige Störungsrechnung bei Entartung (eq math.1750.17)

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Zeitunabhängige Störungsrechnung bei Entartung Eq: math.1750.17

Hash: 2d5ea5e6d1d892c3d2e623450ea1d957

TeX (original user input):

\begin{align}

& \left\langle  k,\beta  \right|\left( {{{\hat{H}}}^{(0)}}-{{E}_{k}}^{(0)} \right)\left| {{\Psi }_{k}}^{(1)} \right\rangle =\sum\limits_{\alpha }{{{c}_{\alpha }}\left( \left\langle  k,\beta   |  k,\alpha  \right\rangle {{E}_{k}}^{(1)}-\left\langle  k,\beta  \right|\hat{V}\left| k,\alpha  \right\rangle  \right)} \\

& \left\langle  k,\beta  \right|\left( {{{\hat{H}}}^{(0)}}-{{E}_{k}}^{(0)} \right)\left| {{\Psi }_{k}}^{(1)} \right\rangle =0 \\

& \left\langle  k,\beta   |  k,\alpha  \right\rangle ={{\delta }_{\beta \alpha }} \\

& \left\langle  k,\beta  \right|\hat{V}\left| k,\alpha  \right\rangle :={{{\hat{V}}}_{\beta \alpha }} \\

\end{align}

TeX (checked):

{\begin{aligned}&\left\langle k,\beta \right|\left({{\hat {H}}^{(0)}}-{{E}_{k}}^{(0)}\right)\left|{{\Psi }_{k}}^{(1)}\right\rangle =\sum \limits _{\alpha }{{{c}_{\alpha }}\left(\left\langle k,\beta |k,\alpha \right\rangle {{E}_{k}}^{(1)}-\left\langle k,\beta \right|{\hat {V}}\left|k,\alpha \right\rangle \right)}\\&\left\langle k,\beta \right|\left({{\hat {H}}^{(0)}}-{{E}_{k}}^{(0)}\right)\left|{{\Psi }_{k}}^{(1)}\right\rangle =0\\&\left\langle k,\beta |k,\alpha \right\rangle ={{\delta }_{\beta \alpha }}\\&\left\langle k,\beta \right|{\hat {V}}\left|k,\alpha \right\rangle :={{\hat {V}}_{\beta \alpha }}\\\end{aligned}}

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\begin{matrix} ⟨ k, β | ({\hat{H}}^{(0)} - {E_{k}}^{(0)}) | {Ψ_{k}}^{(1)} ⟩ = \sum_{α} c_{α} (⟨ k, β | k, α ⟩ {E_{k}}^{(1)} - ⟨ k, β | \hat{V} | k, α ⟩) \\ ⟨ k, β | ({\hat{H}}^{(0)} - {E_{k}}^{(0)}) | {Ψ_{k}}^{(1)} ⟩ = 0 \\ ⟨ k, β | k, α ⟩ = δ_{β α} \\ ⟨ k, β | \hat{V} | k, α ⟩ := {\hat{V}}_{β α} \end{matrix}

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Identifiers

$k$

$β$

$\hat{H}$

$E_{k}$

$Ψ_{k}$

$α$

$c_{α}$

$k$

$β$

$k$

$α$

$E_{k}$

$k$

$β$

$\hat{V}$

$k$

$α$

$k$

$β$

$\hat{H}$

$E_{k}$

$Ψ_{k}$

$k$

$β$

$k$

$α$

$δ_{β α}$

$k$

$β$

$\hat{V}$

$k$

$α$

${\hat{V}}_{β α}$

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