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Display information for equation id:math.1807.54 on revision:1807

* Page found: Dirac- Gleichung für Elektronen (eq math.1807.54)

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TeX (original user input): 

\begin{align}

& i\hbar \dot{\Psi }=-i\hbar c{{\alpha }^{\mu }}{{\partial }_{\mu }}\Psi +{{m}_{0}}{{c}^{2}}\beta \Psi  \\

& -i\hbar {{{\dot{\Psi }}}^{+}}=i\hbar c{{\left( {{\alpha }^{\mu }}{{\partial }_{\mu }}\Psi  \right)}^{+}}+{{m}_{0}}{{c}^{2}}{{\left( \beta \Psi  \right)}^{+}} \\

& {{\left( \beta \Psi  \right)}^{+}}={{\Psi }^{+}}\beta  \\

& {{\left( {{\alpha }^{\mu }}{{\partial }_{\mu }}\Psi  \right)}^{+}}=\left( {{\partial }_{\mu }}{{\Psi }^{+}} \right){{\alpha }^{\mu }} \\

\end{align}

TeX (checked): 

{\begin{aligned}&i\hbar {\dot {\Psi }}=-i\hbar c{{\alpha }^{\mu }}{{\partial }_{\mu }}\Psi +{{m}_{0}}{{c}^{2}}\beta \Psi \\&-i\hbar {{\dot {\Psi }}^{+}}=i\hbar c{{\left({{\alpha }^{\mu }}{{\partial }_{\mu }}\Psi \right)}^{+}}+{{m}_{0}}{{c}^{2}}{{\left(\beta \Psi \right)}^{+}}\\&{{\left(\beta \Psi \right)}^{+}}={{\Psi }^{+}}\beta \\&{{\left({{\alpha }^{\mu }}{{\partial }_{\mu }}\Psi \right)}^{+}}=\left({{\partial }_{\mu }}{{\Psi }^{+}}\right){{\alpha }^{\mu }}\\\end{aligned}}

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MathML (32.792 KB / 3.689 KB) :

i ⁢ ℏ ⁢ Ψ ˙ = - i ⁢ ℏ ⁢ c ⁢ α μ ⁢ ∂ μ ⁡ Ψ + m 0 ⁢ c 2 ⁢ β ⁢ Ψ - i ⁢ ℏ ⁢ Ψ ˙ + = i ⁢ ℏ ⁢ c ⁢ ( α μ ⁢ ∂ μ ⁡ Ψ ) + + m 0 ⁢ c 2 ⁢ ( β ⁢ Ψ ) + ( β ⁢ Ψ ) + = Ψ + ⁢ β ( α μ ⁢ ∂ μ ⁡ Ψ ) + = ( ∂ μ ⁡ Ψ + ) ⁢ α μ absent 𝑖 Planck-constant-over-2-pi ˙ Ψ 𝑖 Planck-constant-over-2-pi 𝑐 superscript 𝛼 𝜇 subscript 𝜇 Ψ subscript 𝑚 0 superscript 𝑐 2 𝛽 Ψ absent 𝑖 Planck-constant-over-2-pi superscript ˙ Ψ 𝑖 Planck-constant-over-2-pi 𝑐 superscript superscript 𝛼 𝜇 subscript 𝜇 Ψ subscript 𝑚 0 superscript 𝑐 2 superscript 𝛽 Ψ absent superscript 𝛽 Ψ superscript Ψ 𝛽 absent superscript superscript 𝛼 𝜇 subscript 𝜇 Ψ subscript 𝜇 superscript Ψ superscript 𝛼 𝜇 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle i\hbar\dot{\Psi% }=-i\hbar c{{\alpha}^{\mu}}{{\partial}_{\mu}}\Psi+{{m}_{0}}{{c}^{2}}\beta\Psi% \\ \par&\displaystyle-i\hbar{{{\dot{\Psi}}}^{+}}=i\hbar c{{\left({{\alpha}^{\mu}}% {{\partial}_{\mu}}\Psi\right)}^{+}}+{{m}_{0}}{{c}^{2}}{{\left(\beta\Psi\right)% }^{+}}\\ \par&\displaystyle{{\left(\beta\Psi\right)}^{+}}={{\Psi}^{+}}\beta\\ \par&\displaystyle{{\left({{\alpha}^{\mu}}{{\partial}_{\mu}}\Psi\right)}^{+}}=% \left({{\partial}_{\mu}}{{\Psi}^{+}}\right){{\alpha}^{\mu}}\\ \par\end{aligned}}}

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MathML (3.359 KB / 495 B) :

iℏΨ˙=−iℏcαμ∂μΨ+m0c2βΨ−iℏΨ˙+=iℏc(αμ∂μΨ)++m0c2(βΨ)+(βΨ)+=Ψ+β(αμ∂μΨ)+=(∂μΨ+)αμ

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