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Display information for equation id:math.1737.6 on revision:1737
* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1737.6)
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TeX (original user input):
\begin{align}
& \hat{H}={{{\hat{H}}}_{0}}-\frac{e}{m}\bar{A}\cdot \hat{\bar{p}}={{{\hat{H}}}_{0}}+{{{\hat{H}}}^{1}} \\
& {{{\hat{H}}}^{1}}:=-\frac{e}{m}\cos (\bar{k}\bar{r}-\omega t){{{\bar{A}}}_{0}}\hat{\bar{p}}=-\frac{e}{2m}{{e}^{i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}{{e}^{-i\omega t}}-\frac{e}{2m}{{e}^{-i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}{{e}^{i\omega t}} \\
& -\frac{e}{2m}{{e}^{i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}:=\hat{F} \\
& -\frac{e}{2m}{{e}^{-i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}:={{{\hat{F}}}^{+}} \\
& {{{\hat{H}}}^{1}}=\hat{F}{{e}^{-i\omega t}}+{{{\hat{F}}}^{+}}{{e}^{i\omega t}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\hat {H}}={{\hat {H}}_{0}}-{\frac {e}{m}}{\bar {A}}\cdot {\hat {\bar {p}}}={{\hat {H}}_{0}}+{{\hat {H}}^{1}}\\&{{\hat {H}}^{1}}:=-{\frac {e}{m}}\cos({\bar {k}}{\bar {r}}-\omega t){{\bar {A}}_{0}}{\hat {\bar {p}}}=-{\frac {e}{2m}}{{e}^{i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}{{e}^{-i\omega t}}-{\frac {e}{2m}}{{e}^{-i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}{{e}^{i\omega t}}\\&-{\frac {e}{2m}}{{e}^{i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}:={\hat {F}}\\&-{\frac {e}{2m}}{{e}^{-i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}:={{\hat {F}}^{+}}\\&{{\hat {H}}^{1}}={\hat {F}}{{e}^{-i\omega t}}+{{\hat {F}}^{+}}{{e}^{i\omega t}}\\\end{aligned}}
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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><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mi>:</mi><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></mfrac></mrow><mi>cos</mi><mo>⁡</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>−</mo><mi>ω</mi><mi>t</mi><mo stretchy="false">)</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><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><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mrow data-mjx-texclass="ORD"><mrow 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data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><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><mi>:</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>^</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>i</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow></msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><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><mi>:</mi><mo>=</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>^</mo></mover></mrow></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>i</mi><mi>ω</mi><mi>t</mi></mrow></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>ω</mi><mi>t</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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