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Display information for equation id:math.2711.118 on revision:2711
* Page found: Formaler Aufbau der Quantenmechanik (eq math.2711.118)
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Hash: 7380118f525feff725dc538c7381fc54
TeX (original user input):
{{\left\langle {\hat{A}} \right\rangle }_{t}}=\left\langle \Psi \left( 0 \right){{e}^{\mathfrak{i} \hat{H}t}}\,\left| \hat{A}\, \right|\,{{e}^{-\mathfrak{i} \hat{H}t}}\Psi \left( 0 \right) \right\rangle =\left\langle \Psi \left( 0 \right)\,\underbrace{\left| {{e}^{\mathfrak{i} \hat{H}t}}\hat{A}{{e}^{-\mathfrak{i} \hat{H}t}} \right|}_{\tilde{A}}\,\Psi \left( 0 \right) \right\rangle
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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>A</mi><mo>^</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub></mstyle><mo>=</mo><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><mn>0</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mi>t</mi></mrow></mrow></msup><mspace width="0.167em"></mspace><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>^</mo></mover></mrow></mrow><mspace width="0.167em"></mspace><mo data-mjx-texclass="CLOSE">|</mo></mrow><mspace width="0.167em"></mspace><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mi>t</mi></mrow></mrow></msup><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><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><mn>0</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="0.167em"></mspace><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mi>t</mi></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>^</mo></mover></mrow></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mi>t</mi></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>~</mo></mover></mrow></mrow></mrow></munder><mspace width="0.167em"></mspace><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mrow></math>
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