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Display information for equation id:math.1632.13 on revision:1632
* Page found: Eigenwerte und Eigenzustände von hermiteschen Operatoren (eq math.1632.13)
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\begin{align}
& \left\langle {{\Psi }_{1}} \right|\hat{F}\left| {{\Psi }_{2}} \right\rangle ={{F}_{2}}\left\langle {{\Psi }_{1}} | {{\Psi }_{2}} \right\rangle \\
& \left\langle {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle ={{F}_{1}}\left\langle {{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle =\left\langle {{\Psi }_{1}} \right|\hat{F}\left| {{\Psi }_{2}} \right\rangle *={{F}_{2}}\left\langle {{\Psi }_{1}} | {{\Psi }_{2}} \right\rangle \quad falls\ \hat{F}={{{\hat{F}}}^{+}},{{F}_{2}}={{F}_{2}}* \\
& \left\langle {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle =\left\langle {{{\hat{F}}}^{+}}{{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle ={{F}_{2}}\left\langle {{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle \\
& \left\langle {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle -\left\langle {{\Psi }_{2}} \right|\hat{F}\left| {{\Psi }_{1}} \right\rangle =\left( {{F}_{2}}-{{F}_{1}} \right)\left\langle {{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle \\
\end{align}
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data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow 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