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Display information for equation id:math.1598.15 on revision:1598

* Page found: Zeitunabhängige Schrödinger- Gleichung und stationäre Zustände (eq math.1598.15)

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\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 ¯ ^ ) ⟩ = ∫ Ψ E * ( r ¯ , t ) ⁢ F ⁢ ( p ¯ ^ , r ¯ ^ ) ⁢ Ψ E ⁢ ( r ¯ , t ) ⁢ d 3 ⁢ r = ∫ ϕ E ⁢ ( r ¯ ) * F ⁢ ( p ¯ ^ , r ¯ ^ ) ⁢ ϕ E ⁢ ( r ¯ ) = ∫ ϕ E ⁢ ( r ¯ ) * F ⁢ ( ℏ i ⁢ ∇ , r ¯ ^ ) ⁢ ϕ E ⁢ ( r ¯ ) delimited-⟨⟩ 𝐹 ^ ¯ 𝑝 ^ ¯ 𝑟 subscript Ψ 𝐸 ¯ 𝑟 𝑡 𝐹 ^ ¯ 𝑝 ^ ¯ 𝑟 subscript Ψ 𝐸 ¯ 𝑟 𝑡 superscript 𝑑 3 𝑟 subscript italic-ϕ 𝐸 ¯ 𝑟 𝐹 ^ ¯ 𝑝 ^ ¯ 𝑟 subscript italic-ϕ 𝐸 ¯ 𝑟 subscript italic-ϕ 𝐸 ¯ 𝑟 𝐹 Planck-constant-over-2-pi 𝑖 ∇ ^ ¯ 𝑟 subscript italic-ϕ 𝐸 ¯ 𝑟 {\displaystyle{\displaystyle\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(ℏi∇,r¯^)ϕE(r¯)

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