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Display information for equation id:math.1593.3 on revision:1593

* Page found: Kontinuitätsgleichung (Quantenmechnik) (eq math.1593.3)

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TeX (original user input): 

i\hbar \dot{\Psi }*(\bar{r},t)=\frac{1}{2m}\left[ -{{\hbar }^{2}}\Delta \Psi *-i\hbar e\nabla \left( \bar{A}\Psi * \right)-i\hbar e\bar{A}\left( \nabla \Psi * \right)+{{e}^{2}}{{A}^{2}}\Psi * \right]+V\Psi *(\bar{r},t)

TeX (checked): 

i\hbar {\dot {\Psi }}*({\bar {r}},t)={\frac {1}{2m}}\left[-{{\hbar }^{2}}\Delta \Psi *-i\hbar e\nabla \left({\bar {A}}\Psi *\right)-i\hbar e{\bar {A}}\left(\nabla \Psi *\right)+{{e}^{2}}{{A}^{2}}\Psi *\right]+V\Psi *({\bar {r}},t)

LaTeXML (experimentell; verwendet MathML) rendering

MathML (13.108 KB / 2.073 KB) :

i ℏ Ψ ˙ * ( r ¯ , t ) = 1 2 ⁢ m [ - ℏ 2 Δ Ψ * - i ℏ e ∇ ( A ¯ Ψ * ) - i ℏ e A ¯ ( ∇ Ψ * ) + e 2 A 2 Ψ * ] + V Ψ * ( r ¯ , t ) fragments i Planck-constant-over-2-pi ˙ Ψ fragments ( ¯ 𝑟 , t ) 1 2 𝑚 fragments [ superscript Planck-constant-over-2-pi 2 Δ Ψ i Planck-constant-over-2-pi e ∇ fragments ( ¯ 𝐴 Ψ ) i Planck-constant-over-2-pi e ¯ 𝐴 fragments ( ∇ Ψ ) superscript 𝑒 2 superscript 𝐴 2 Ψ ] V Ψ fragments ( ¯ 𝑟 , t ) {\displaystyle{\displaystyle i\hbar\dot{\Psi}*(\bar{r},t)=\frac{1}{2m}\left[-{% {\hbar}^{2}}\Delta\Psi*-i\hbar e\nabla\left(\bar{A}\Psi*\right)-i\hbar e\bar{A% }\left(\nabla\Psi*\right)+{{e}^{2}}{{A}^{2}}\Psi*\right]+V\Psi*(\bar{r},t)}}

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MathML (2.231 KB / 439 B) :

iℏΨ˙*(r¯,t)=12m[−ℏ2ΔΨ*−iℏe∇(A¯Ψ*)−iℏeA¯(∇Ψ*)+e2A2Ψ*]+VΨ*(r¯,t)

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Calculated based on the variables occurring on the entire Kontinuitätsgleichung (Quantenmechnik) page

Identifiers

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