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* Page found: Schrödingergleichung mit äußeren Potenzialen (eq math.1586.83)

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Schrödingergleichung mit äußeren Potenzialen Eq: math.1587.83

Hash: baf5bd7c54185c4a24af8b44adfa0196

TeX (original user input):

\begin{align}
& \Psi ({{{\bar{r}}}_{s}})={{\Psi }_{1}}\acute{\ }{{e}^{-i\frac{e}{\hbar }\int\limits_{1}^{{}}{\bar{A}(\bar{s})d\bar{s}}}}+{{\Psi }_{2}}\acute{\ }{{e}^{-i\frac{e}{\hbar }\int\limits_{2}^{{}}{\bar{A}(\bar{s})d\bar{s}}}}=\left( {{\Psi }_{1}}\acute{\ }({{{\bar{r}}}_{s}},t){{e}^{i\frac{e}{\hbar }\int\limits_{2}^{{}}{\bar{A}(\bar{s})d\bar{s}}-i\frac{e}{\hbar }\int\limits_{1}^{{}}{\bar{A}(\bar{s})d\bar{s}}}}+{{\Psi }_{2}}\acute{\ }({{{\bar{r}}}_{s}},t) \right){{e}^{-i\frac{e}{\hbar }\int\limits_{2}^{{}}{\bar{A}(\bar{s})d\bar{s}}}} \\
& =\left( {{\Psi }_{1}}\acute{\ }({{{\bar{r}}}_{s}},t){{e}^{-i\frac{e}{\hbar }\oint\limits_{{}}{\bar{A}(\bar{s})d\bar{s}}}}+{{\Psi }_{2}}\acute{\ }({{{\bar{r}}}_{s}},t) \right){{e}^{-i\frac{e}{\hbar }\int\limits_{2}^{{}}{\bar{A}(\bar{s})d\bar{s}}}}=\left( {{\Psi }_{1}}\acute{\ }({{{\bar{r}}}_{s}},t){{e}^{-i\frac{e}{\hbar }\int\limits_{{}}^{{}}{d\bar{f}\ rot\bar{A}}}}+{{\Psi }_{2}}\acute{\ }({{{\bar{r}}}_{s}},t) \right){{e}^{-i\frac{e}{\hbar }\int\limits_{2}^{{}}{\bar{A}(\bar{s})d\bar{s}}}} \\
& =\left( {{\Psi }_{1}}\acute{\ }({{{\bar{r}}}_{s}},t){{e}^{-i\frac{e}{\hbar }\int\limits_{{}}^{{}}{\bar{B}d\bar{f}}}}+{{\Psi }_{2}}\acute{\ }({{{\bar{r}}}_{s}},t) \right){{e}^{-i\frac{e}{\hbar }\int\limits_{2}^{{}}{\bar{A}(\bar{s})d\bar{s}}}}=\left( {{\Psi }_{1}}\acute{\ }({{{\bar{r}}}_{s}},t){{e}^{-i\frac{e}{\hbar }{{\Phi }_{B}}}}+{{\Psi }_{2}}\acute{\ }({{{\bar{r}}}_{s}},t) \right){{e}^{-i\frac{e}{\hbar }\int\limits_{2}^{{}}{\bar{A}(\bar{s})d\bar{s}}}} \\
\end{align}

TeX (checked):

{\begin{aligned}&\Psi ({{\bar {r}}_{s}})={{\Psi }_{1}}{\acute {\ }}{{e}^{-i{\frac {e}{\hbar }}\int \limits _{1}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}+{{\Psi }_{2}}{\acute {\ }}{{e}^{-i{\frac {e}{\hbar }}\int \limits _{2}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}=\left({{\Psi }_{1}}{\acute {\ }}({{\bar {r}}_{s}},t){{e}^{i{\frac {e}{\hbar }}\int \limits _{2}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}-i{\frac {e}{\hbar }}\int \limits _{1}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}+{{\Psi }_{2}}{\acute {\ }}({{\bar {r}}_{s}},t)\right){{e}^{-i{\frac {e}{\hbar }}\int \limits _{2}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}\\&=\left({{\Psi }_{1}}{\acute {\ }}({{\bar {r}}_{s}},t){{e}^{-i{\frac {e}{\hbar }}\oint \limits _{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}+{{\Psi }_{2}}{\acute {\ }}({{\bar {r}}_{s}},t)\right){{e}^{-i{\frac {e}{\hbar }}\int \limits _{2}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}=\left({{\Psi }_{1}}{\acute {\ }}({{\bar {r}}_{s}},t){{e}^{-i{\frac {e}{\hbar }}\int \limits _{}^{}{d{\bar {f}}\ rot{\bar {A}}}}}+{{\Psi }_{2}}{\acute {\ }}({{\bar {r}}_{s}},t)\right){{e}^{-i{\frac {e}{\hbar }}\int \limits _{2}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}\\&=\left({{\Psi }_{1}}{\acute {\ }}({{\bar {r}}_{s}},t){{e}^{-i{\frac {e}{\hbar }}\int \limits _{}^{}{{\bar {B}}d{\bar {f}}}}}+{{\Psi }_{2}}{\acute {\ }}({{\bar {r}}_{s}},t)\right){{e}^{-i{\frac {e}{\hbar }}\int \limits _{2}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}=\left({{\Psi }_{1}}{\acute {\ }}({{\bar {r}}_{s}},t){{e}^{-i{\frac {e}{\hbar }}{{\Phi }_{B}}}}+{{\Psi }_{2}}{\acute {\ }}({{\bar {r}}_{s}},t)\right){{e}^{-i{\frac {e}{\hbar }}\int \limits _{2}^{}{{\bar {A}}({\bar {s}})d{\bar {s}}}}}\\\end{aligned}}

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\begin{aligned} Ψ ({\bar{r}}_{s}) = Ψ_{1} \overset{´}{} e^{- i \frac{e}{ℏ} \int_{1}^{} \bar{A} (\bar{s}) d \bar{s}} + Ψ_{2} \overset{´}{} e^{- i \frac{e}{ℏ} \int_{2}^{} \bar{A} (\bar{s}) d \bar{s}} = (Ψ_{1} \overset{´}{} ({\bar{r}}_{s}, t) e^{i \frac{e}{ℏ} \int_{2}^{} \bar{A} (\bar{s}) d \bar{s} - i \frac{e}{ℏ} \int_{1}^{} \bar{A} (\bar{s}) d \bar{s}} + Ψ_{2} \overset{´}{} ({\bar{r}}_{s}, t)) e^{- i \frac{e}{ℏ} \int_{2}^{} \bar{A} (\bar{s}) d \bar{s}} \\ = (Ψ_{1} \overset{´}{} ({\bar{r}}_{s}, t) e^{- i \frac{e}{ℏ} \oint_{} \bar{A} (\bar{s}) d \bar{s}} + Ψ_{2} \overset{´}{} ({\bar{r}}_{s}, t)) e^{- i \frac{e}{ℏ} \int_{2}^{} \bar{A} (\bar{s}) d \bar{s}} = (Ψ_{1} \overset{´}{} ({\bar{r}}_{s}, t) e^{- i \frac{e}{ℏ} \int_{}^{} d \bar{f} r o t \bar{A}} + Ψ_{2} \overset{´}{} ({\bar{r}}_{s}, t)) e^{- i \frac{e}{ℏ} \int_{2}^{} \bar{A} (\bar{s}) d \bar{s}} \\ = (Ψ_{1} \overset{´}{} ({\bar{r}}_{s}, t) e^{- i \frac{e}{ℏ} \int_{}^{} \bar{B} d \bar{f}} + Ψ_{2} \overset{´}{} ({\bar{r}}_{s}, t)) e^{- i \frac{e}{ℏ} \int_{2}^{} \bar{A} (\bar{s}) d \bar{s}} = (Ψ_{1} \overset{´}{} ({\bar{r}}_{s}, t) e^{- i \frac{e}{ℏ} Φ_{B}} + Ψ_{2} \overset{´}{} ({\bar{r}}_{s}, t)) e^{- i \frac{e}{ℏ} \int_{2}^{} \bar{A} (\bar{s}) d \bar{s}} \end{aligned}

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data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi>i</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>f</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></mrow></msup><mo>+</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi>i</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></mrow></msup><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi>i</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi></mrow></mfrac></mrow><msub><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow></msub></mrow></mrow></msup><mo>+</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi>i</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$Ψ$

${\bar{r}}_{s}$

$Ψ_{1}$

$\overset{´}{}$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$Ψ_{2}$

$\overset{´}{}$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$Ψ_{1}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$Ψ_{2}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$Ψ_{1}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$d$

$\bar{s}$

$Ψ_{2}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$Ψ_{1}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{f}$

$r$

$o$

$t$

$\bar{A}$

$Ψ_{2}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$Ψ_{1}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{B}$

$\bar{f}$

$Ψ_{2}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

$Ψ_{1}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$Φ_{B}$

$Ψ_{2}$

$\overset{´}{}$

${\bar{r}}_{s}$

$t$

$e$

$i$

$e$

$\bar{A}$

$\bar{s}$

$\bar{s}$

MathML observations

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General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

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MathML observations

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General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

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