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Display information for equation id:math.2711.75 on revision:2711
* Page found: Formaler Aufbau der Quantenmechanik (eq math.2711.75)
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Hash: 3288795258a087f4fba106d3da8ae608
TeX (original user input):
{{\left\langle {\hat{x}} \right\rangle }_{n}}=\int\limits_{-\infty }^{\infty }{{{\Psi }_{n}}^{*}\left( x \right){{x}^{2}}{{\Psi }_{n}}\left( x \right)dx=}\int\limits_{-\infty }^{\infty }{{{x}^{2}}\underbrace{{{\left| \Psi \left( x \right) \right|}^{2}}}_{\text{Wahrscheinlichkeitsdichte}}dx}
TeX (checked):
{{\left\langle {\hat {x}}\right\rangle }_{n}}=\int \limits _{-\infty }^{\infty }{{{\Psi }_{n}}^{*}\left(x\right){{x}^{2}}{{\Psi }_{n}}\left(x\right)dx=}\int \limits _{-\infty }^{\infty }{{{x}^{2}}\underbrace {{\left|\Psi \left(x\right)\right|}^{2}} _{\text{Wahrscheinlichkeitsdichte}}dx}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>^</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mstyle><mo>=</mo><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><msup><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mo>*</mo></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>d</mi><mi>x</mi><mo>=</mo></mrow><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><munder><mrow data-mjx-texclass="OP"><munder><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>x</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>Wahrscheinlichkeitsdichte</mtext></mrow></mrow></munder><mi>d</mi><mi>x</mi></mrow></mrow></math>
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