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Display information for equation id:math.1597.15 on revision:1597

* Page found: Zeitunabhängige Schrödinger- Gleichung und stationäre Zustände (eq math.1597.15)

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Hash: 01be725eda8883c170d10de39ab9f363

TeX (original user input):

\left\langle F(\hat{\bar{p}},\hat{\bar{r}}) \right\rangle =\int_{{}}^{{}}{{}}{{\Psi }_{E}}*(\bar{r},t)F(\hat{\bar{p}},\hat{\bar{r}}){{\Psi }_{E}}(\bar{r},t){{d}^{3}}r=\int_{{}}^{{}}{{{\phi }_{E}}(\bar{r})*}F(\hat{\bar{p}},\hat{\bar{r}}){{\phi }_{E}}(\bar{r})=\int_{{}}^{{}}{{{\phi }_{E}}(\bar{r})*}F(\frac{\hbar }{i}\nabla ,\hat{\bar{r}}){{\phi }_{E}}(\bar{r})

TeX (checked):

\left\langle F({\hat {\bar {p}}},{\hat {\bar {r}}})\right\rangle =\int _{}^{}{}{{\Psi }_{E}}*({\bar {r}},t)F({\hat {\bar {p}}},{\hat {\bar {r}}}){{\Psi }_{E}}({\bar {r}},t){{d}^{3}}r=\int _{}^{}{{{\phi }_{E}}({\bar {r}})*}F({\hat {\bar {p}}},{\hat {\bar {r}}}){{\phi }_{E}}({\bar {r}})=\int _{}^{}{{{\phi }_{E}}({\bar {r}})*}F({\frac {\hbar }{i}}\nabla ,{\hat {\bar {r}}}){{\phi }_{E}}({\bar {r}})

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F(p¯^,r¯^)=ΨE*(r¯,t)F(p¯^,r¯^)ΨE(r¯,t)d3r=ϕE(r¯)*F(p¯^,r¯^)ϕE(r¯)=ϕE(r¯)*F(i,r¯^)ϕE(r¯)
<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">&#x27E8;</mo><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>^</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>^</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mo>*</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>^</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>^</mo></mover></mrow></mrow><mo stretchy="false">)</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></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>,</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msub><mi>&#x03D5;</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></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></mrow><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>^</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>^</mo></mover></mrow></mrow><mo stretchy="false">)</mo><msub><mi>&#x03D5;</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></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">&#x222B;</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msub><mi>&#x03D5;</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></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></mrow><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></mfrac></mrow><mi mathvariant="normal">&#x2207;</mi><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>^</mo></mover></mrow></mrow><mo stretchy="false">)</mo><msub><mi>&#x03D5;</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></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></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Zeitunabhängige Schrödinger- Gleichung und stationäre Zustände page

Identifiers

  • F
  • p¯^
  • r¯^
  • ΨE
  • r¯
  • t
  • F
  • p¯^
  • r¯^
  • ΨE
  • r¯
  • t
  • r
  • ϕE
  • r¯
  • F
  • p¯^
  • r¯^
  • ϕE
  • r¯
  • ϕE
  • r¯
  • F
  • i
  • r¯^
  • ϕE
  • r¯

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