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Display information for equation id:math.1805.28 on revision:1805

* Page found: Dirac- Gleichung für Elektronen (eq math.1805.28)

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Dirac- Gleichung für Elektronen Eq: math.1807.28

Hash: 5474fa48513c42092cddda55a923d90d

TeX (original user input):

\begin{align}

& -{{\hbar }^{2}}\frac{{{\partial }^{2}}}{\partial {{t}^{2}}}\Psi =\left[ {{c}^{2}}{{p}^{2}}+{{m}_{0}}^{2}{{c}^{4}} \right]\Psi  \\

& \Rightarrow \left( {{c}^{2}}\sum\limits_{\mu ,\nu =1}^{3}{{}}\left( {{\alpha }^{\mu }}{{\alpha }^{\nu }}{{p}^{\mu }}{{p}^{\nu }} \right)+{{m}_{0}}{{c}^{3}}\sum\limits_{\mu =1}^{3}{{}}\left( {{\alpha }^{\mu }}\beta +\beta {{\alpha }^{\mu }} \right){{p}^{\mu }}+{{m}_{0}}^{2}{{c}^{4}}{{\beta }^{2}} \right)\Psi =\left[ {{c}^{2}}{{p}^{2}}+{{m}_{0}}^{2}{{c}^{4}} \right]\Psi  \\

\end{align}

TeX (checked):

{\begin{aligned}&-{{\hbar }^{2}}{\frac {{\partial }^{2}}{\partial {{t}^{2}}}}\Psi =\left[{{c}^{2}}{{p}^{2}}+{{m}_{0}}^{2}{{c}^{4}}\right]\Psi \\&\Rightarrow \left({{c}^{2}}\sum \limits _{\mu ,\nu =1}^{3}{}\left({{\alpha }^{\mu }}{{\alpha }^{\nu }}{{p}^{\mu }}{{p}^{\nu }}\right)+{{m}_{0}}{{c}^{3}}\sum \limits _{\mu =1}^{3}{}\left({{\alpha }^{\mu }}\beta +\beta {{\alpha }^{\mu }}\right){{p}^{\mu }}+{{m}_{0}}^{2}{{c}^{4}}{{\beta }^{2}}\right)\Psi =\left[{{c}^{2}}{{p}^{2}}+{{m}_{0}}^{2}{{c}^{4}}\right]\Psi \\\end{aligned}}

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\begin{aligned} - ℏ^{2} \frac{\partial^{2}}{\partial t^{2}} Ψ = [c^{2} p^{2} + {m_{0}}^{2} c^{4}] Ψ \\ \Rightarrow (c^{2} \sum_{μ, ν = 1}^{3} (α^{μ} α^{ν} p^{μ} p^{ν}) + m_{0} c^{3} \sum_{μ = 1}^{3} (α^{μ} β + β α^{μ}) p^{μ} + {m_{0}}^{2} c^{4} β^{2}) Ψ = [c^{2} p^{2} + {m_{0}}^{2} c^{4}] Ψ \end{aligned}

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$Ψ$

$c$

$p$

$m_{0}$

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$Ψ$

$c$

$μ$

$ν$

$α$

$μ$

$α$

$ν$

$p$

$μ$

$p$

$ν$

$m_{0}$

$c$

$μ$

$α$

$μ$

$β$

$β$

$α$

$μ$

$p$

$μ$

$m_{0}$

$c$

$β$

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$c$

$p$

$m_{0}$

$c$

$Ψ$

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