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Display information for equation id:math.1822.46 on revision:1822

* Page found: Das Wasserstoffatom (relativistsich) (eq math.1822.46)

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Das Wasserstoffatom (relativistsich) Eq: math.1826.46

Hash: 467b0756b9e72b1396c36b42b0cb7e55

TeX (original user input):

\begin{align}

& F(\rho )={{\rho }^{\lambda }}{{e}^{-\rho }}f\left( \rho  \right) \\

& G(\rho )={{\rho }^{\lambda }}{{e}^{-\rho }}g\left( \rho  \right) \\

& \Rightarrow g\acute{\ }-g+\frac{\lambda +q}{\rho }g-\left( \frac{{{a}_{2}}}{a}-\frac{\gamma }{\rho } \right)f=0 \\

& f\acute{\ }-f+\frac{\lambda -q}{\rho }f-\left( \frac{{{a}_{1}}}{a}+\frac{\gamma }{\rho } \right)g=0 \\

\end{align}

TeX (checked):

{\begin{aligned}&F(\rho )={{\rho }^{\lambda }}{{e}^{-\rho }}f\left(\rho \right)\\&G(\rho )={{\rho }^{\lambda }}{{e}^{-\rho }}g\left(\rho \right)\\&\Rightarrow g{\acute {\ }}-g+{\frac {\lambda +q}{\rho }}g-\left({\frac {{a}_{2}}{a}}-{\frac {\gamma }{\rho }}\right)f=0\\&f{\acute {\ }}-f+{\frac {\lambda -q}{\rho }}f-\left({\frac {{a}_{1}}{a}}+{\frac {\gamma }{\rho }}\right)g=0\\\end{aligned}}

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MathML (3.402 KB / 510 B) :

\begin{matrix} F (ρ) = ρ^{λ} e^{- ρ} f (ρ) \\ G (ρ) = ρ^{λ} e^{- ρ} g (ρ) \\ \Rightarrow g \overset{´}{} - g + \frac{λ + q}{ρ} g - (\frac{a_{2}}{a} - \frac{γ}{ρ}) f = 0 \\ f \overset{´}{} - f + \frac{λ - q}{ρ} f - (\frac{a_{1}}{a} + \frac{γ}{ρ}) g = 0 \end{matrix}

<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"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>F</mi><mo stretchy="false">(</mo><mi>ρ</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msup><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mi>λ</mi></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>ρ</mi></mrow></mrow></msup><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ρ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>G</mi><mo stretchy="false">(</mo><mi>ρ</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msup><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mi>λ</mi></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>ρ</mi></mrow></mrow></msup><mi>g</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ρ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>g</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">−</mo><mi>g</mi><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>λ</mi><mo stretchy="false">+</mo><mi>q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></mfrac></mrow><mi>g</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></mfrac></mrow><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>γ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>f</mi><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>f</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">−</mo><mi>f</mi><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>λ</mi><mo stretchy="false">−</mo><mi>q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></mfrac></mrow><mi>f</mi><mo stretchy="false">−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></mfrac></mrow><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>γ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>g</mi><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$F$

$ρ$

$ρ$

$λ$

$e$

$ρ$

$f$

$ρ$

$G$

$ρ$

$ρ$

$λ$

$e$

$ρ$

$g$

$ρ$

$g$

$\overset{´}{}$

$g$

$λ$

$q$

$ρ$

$g$

$a_{2}$

$a$

$γ$

$ρ$

$f$

$f$

$\overset{´}{}$

$f$

$λ$

$q$

$ρ$

$f$

$a_{1}$

$a$

$γ$

$ρ$

$g$

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