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Display information for equation id:math.1619.90 on revision:1619
* Page found: Zustandsvektoren im Hilbertraum (eq math.1619.90)
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Hash: f1c8f09ff48c17e1c23f300759a76a03
TeX (original user input):
\left\langle {{\Psi }_{1}} | {{\Psi }_{2}} \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}r\left\langle {{\Psi }_{1}} | {\bar{r}} \right\rangle }\left\langle {\bar{r}} | {{\Psi }_{2}} \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}r}{{\Psi }_{1}}(\bar{r})*{{\Psi }_{2}}(\bar{r})=\int_{{{R}^{3}}}^{{}}{{{d}^{3}}p}{{\tilde{\Psi }}_{1}}(\bar{p})*{{\tilde{\Psi }}_{2}}(\bar{p})
TeX (checked):
\left\langle {{\Psi }_{1}}|{{\Psi }_{2}}\right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}r\left\langle {{\Psi }_{1}}|{\bar {r}}\right\rangle }\left\langle {\bar {r}}|{{\Psi }_{2}}\right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}r}{{\Psi }_{1}}({\bar {r}})*{{\Psi }_{2}}({\bar {r}})=\int _{{R}^{3}}^{}{{{d}^{3}}p}{{\tilde {\Psi }}_{1}}({\bar {p}})*{{\tilde {\Psi }}_{2}}({\bar {p}})
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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"><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>|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><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>|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mo>*</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>p</mi></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Ψ</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mo>*</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Ψ</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo></mstyle></mrow></math>
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