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Display information for equation id:math.1563.47 on revision:1563

* Page found: Kräftefreie Schrödingergleichung (eq math.1563.47)

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TeX (original user input): 

\tilde{\Psi }(k)=\frac{1}{2\pi }\int\limits_{-\frac{\Delta x}{2}}^{\frac{\Delta x}{2}}{dx{{e}^{-ikx}}=}\frac{1}{2\pi }\left. \frac{{{e}^{-ikx}}}{-ik} \right|_{-\frac{\Delta x}{2}}^{\frac{\Delta x}{2}}=\frac{\Delta x}{2\pi }\frac{\sin \left( k\frac{\Delta x}{2} \right)}{k\frac{\Delta x}{2}}

TeX (checked): 

{\tilde {\Psi }}(k)={\frac {1}{2\pi }}\int \limits _{-{\frac {\Delta x}{2}}}^{\frac {\Delta x}{2}}{dx{{e}^{-ikx}}=}{\frac {1}{2\pi }}\left.{\frac {{e}^{-ikx}}{-ik}}\right|_{-{\frac {\Delta x}{2}}}^{\frac {\Delta x}{2}}={\frac {\Delta x}{2\pi }}{\frac {\sin \left(k{\frac {\Delta x}{2}}\right)}{k{\frac {\Delta x}{2}}}}

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MathML (24.921 KB / 3.181 KB) :

Ψ ~ ⁢ ( k ) = 1 2 ⁢ π ⁢ ∫ - Δ ⁢ x 2 Δ ⁢ x 2 𝑑 x ⁢ e - i ⁢ k ⁢ x = 1 2 ⁢ π ⁢ e - i ⁢ k ⁢ x - i ⁢ k | - Δ ⁢ x 2 Δ ⁢ x 2 = Δ ⁢ x 2 ⁢ π ⁢ sin ⁡ ( k ⁢ Δ ⁢ x 2 ) k ⁢ Δ ⁢ x 2 ~ Ψ 𝑘 1 2 𝜋 superscript subscript Δ 𝑥 2 Δ 𝑥 2 differential-d 𝑥 superscript 𝑒 𝑖 𝑘 𝑥 evaluated-at 1 2 𝜋 superscript 𝑒 𝑖 𝑘 𝑥 𝑖 𝑘 Δ 𝑥 2 Δ 𝑥 2 Δ 𝑥 2 𝜋 𝑘 Δ 𝑥 2 𝑘 Δ 𝑥 2 {\displaystyle{\displaystyle\tilde{\Psi}(k)=\frac{1}{2\pi}\int\limits_{-\frac{% \Delta x}{2}}^{\frac{\Delta x}{2}}{dx{{e}^{-ikx}}=}\frac{1}{2\pi}\left.\frac{{% {e}^{-ikx}}}{-ik}\right|_{-\frac{\Delta x}{2}}^{\frac{\Delta x}{2}}=\frac{% \Delta x}{2\pi}\frac{\sin\left(k\frac{\Delta x}{2}\right)}{k\frac{\Delta x}{2}% }}}

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MathML (3.673 KB / 480 B) :

Ψ~(k)=12π∫−Δx2Δx2dxe−ikx=12πe−ikx−ik|−Δx2Δx2=Δx2πsin⁡(kΔx2)kΔx2

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