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Display information for equation id:math.1983.54 on revision:1983

* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1983.54)

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TeX (original user input): 

\Delta {{e}^{\frac{i}{\hbar }W(\bar{r})}}=\nabla \frac{i}{\hbar }\left( \nabla W{{e}^{\frac{i}{\hbar }W(\bar{r})}} \right)\cong -\frac{1}{{{\hbar }^{2}}}{{\left( \nabla W \right)}^{2}}{{e}^{\frac{i}{\hbar }W(\bar{r})}}

TeX (checked): 

\Delta {{e}^{{\frac {i}{\hbar }}W({\bar {r}})}}=\nabla {\frac {i}{\hbar }}\left(\nabla W{{e}^{{\frac {i}{\hbar }}W({\bar {r}})}}\right)\cong -{\frac {1}{{\hbar }^{2}}}{{\left(\nabla W\right)}^{2}}{{e}^{{\frac {i}{\hbar }}W({\bar {r}})}}

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MathML (15.078 KB / 2.121 KB) :

Δ ⁢ e i ℏ ⁢ W ⁢ ( r ¯ ) = ∇ ⁡ i ℏ ⁢ ( ∇ ⁡ W ⁢ e i ℏ ⁢ W ⁢ ( r ¯ ) ) ≅ - 1 ℏ 2 ⁢ ( ∇ ⁡ W ) 2 ⁢ e i ℏ ⁢ W ⁢ ( r ¯ ) Δ superscript 𝑒 𝑖 Planck-constant-over-2-pi 𝑊 ¯ 𝑟 ∇ 𝑖 Planck-constant-over-2-pi ∇ 𝑊 superscript 𝑒 𝑖 Planck-constant-over-2-pi 𝑊 ¯ 𝑟 1 superscript Planck-constant-over-2-pi 2 superscript ∇ 𝑊 2 superscript 𝑒 𝑖 Planck-constant-over-2-pi 𝑊 ¯ 𝑟 {\displaystyle{\displaystyle\Delta{{e}^{\frac{i}{\hbar}W(\bar{r})}}=\nabla% \frac{i}{\hbar}\left(\nabla W{{e}^{\frac{i}{\hbar}W(\bar{r})}}\right)\cong-% \frac{1}{{{\hbar}^{2}}}{{\left(\nabla W\right)}^{2}}{{e}^{\frac{i}{\hbar}W(% \bar{r})}}}}

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MathML (2.363 KB / 397 B) :

ΔeiℏW(r¯)=∇iℏ(∇WeiℏW(r¯))≅−1ℏ2(∇W)2eiℏW(r¯)

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