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Display information for equation id:math.1614.89 on revision:1614

* Page found: Zustandsvektoren im Hilbertraum (eq math.1614.89)

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TeX (original user input):

\left\langle  \Psi  | {\bar{r}} \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}p\left\langle  \Psi  | {\bar{p}} \right\rangle }\left\langle  {\bar{p}} | {\bar{r}} \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}p}\tilde{\Psi }(\bar{p})*{{\left( 2\pi \hbar  \right)}^{-\tfrac{3}{2}}}{{e}^{-\frac{i}{\hbar }\bar{p}\bar{r}}}=\left\langle  {\bar{r}} | \Psi  \right\rangle *=\Psi (\bar{r})*

TeX (checked):

\left\langle \Psi |{\bar {r}}\right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}p\left\langle \Psi |{\bar {p}}\right\rangle }\left\langle {\bar {p}}|{\bar {r}}\right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}p}{\tilde {\Psi }}({\bar {p}})*{{\left(2\pi \hbar \right)}^{-{\tfrac {3}{2}}}}{{e}^{-{\frac {i}{\hbar }}{\bar {p}}{\bar {r}}}}=\left\langle {\bar {r}}|\Psi \right\rangle *=\Psi ({\bar {r}})*

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Ψ|r¯=R3d3pΨ|p¯p¯|r¯=R3d3pΨ~(p¯)(2π)32eip¯r¯=r¯|Ψ=Ψ(r¯)
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mi>Ψ</mi><mo stretchy="false">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE"></mo></mrow><mo stretchy="false">=</mo><msubsup><mo stretchy="false"></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></msubsup><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>p</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mi>Ψ</mi><mo stretchy="false">|</mo><mover><mi>p</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE"></mo></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mover><mi>p</mi><mo>¯</mo></mover><mo stretchy="false">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo data-mjx-texclass="CLOSE"></mo></mrow><mo stretchy="false">=</mo><msubsup><mo stretchy="false"></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></msubsup><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>p</mi></mrow><mover><mi>Ψ</mi><mo>~</mo></mover><mo stretchy="false">(</mo><mover><mi>p</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mo stretchy="false"></mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>π</mi><mi alternate="1"></mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false"></mo><mrow data-mjx-texclass="ORD"><mstyle displaystyle="false" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mstyle></mrow></mrow></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false"></mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"><mi alternate="1"></mi></mrow></mfrac></mrow><mover><mi>p</mi><mo>¯</mo></mover><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow></msup><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">|</mo><mi>Ψ</mi><mo data-mjx-texclass="CLOSE"></mo></mrow><mo stretchy="false"></mo><mo stretchy="false">=</mo><mi>Ψ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mo stretchy="false"></mo></mstyle></mrow></math>

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Identifiers

  • Ψ
  • r¯
  • R
  • p
  • Ψ
  • p¯
  • p¯
  • r¯
  • R
  • p
  • Ψ~
  • p¯
  • π
  • e
  • i
  • p¯
  • r¯
  • r¯
  • Ψ
  • Ψ
  • r¯

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