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Display information for equation id:math.3431.94 on revision:3431

* Page found: Kernkräfte (eq math.3431.94)

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Kernkräfte Eq: math.3436.98

Hash: 165cbeded9910978490991316797b28a

TeX (original user input):

\begin{align}
A_1 \sin Kr_0 &= A_2 \sin (k r_0 +\delta_0) &=A_2 k (r_0-a)\\
K A_1 \cos Kr_0 &= k A_2 \cos (k r_0 +\delta_0) &=A_2 k\\[0.5em]
K \cot Kr_0 &=  \cot (k r_0 +\delta_0) &= \underbrace{(r_0-a)^{-1}}_{k \ll K}\\
\end{align}

TeX (checked):

{\begin{aligned}A_{1}\sin Kr_{0}&=A_{2}\sin(kr_{0}+\delta _{0})&=A_{2}k(r_{0}-a)\\KA_{1}\cos Kr_{0}&=kA_{2}\cos(kr_{0}+\delta _{0})&=A_{2}k\\[0.5em]K\cot Kr_{0}&=\cot(kr_{0}+\delta _{0})&=\underbrace {(r_{0}-a)^{-1}} _{k\ll K}\\\end{aligned}}

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\begin{matrix} A_{1} \sin K r_{0} & = A_{2} \sin (k r_{0} + δ_{0}) & = A_{2} k (r_{0} - a) \\ K A_{1} \cos K r_{0} & = k A_{2} \cos (k r_{0} + δ_{0}) & = A_{2} k \\ K \cot K r_{0} & = \cot (k r_{0} + δ_{0}) & = \underset{k ≪ K}{\underset{⏟}{(r_{0} - a)^{- 1}}} \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"><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>sin</mi><mo>&#x2061;</mo><mi>K</mi><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">=</mo><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>sin</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>k</mi><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mtd><mtd class="mwe-math-columnalign-r"><mo stretchy="false">=</mo><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>k</mi><mo stretchy="false">(</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">−</mo><mi>a</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd style="padding-bottom: 0.5em;" class="mwe-math-columnalign-r"><mi>K</mi><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>cos</mi><mo>&#x2061;</mo><mi>K</mi><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd><mtd style="padding-bottom: 0.5em;" class="mwe-math-columnalign-l"><mo stretchy="false">=</mo><mi>k</mi><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>cos</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>k</mi><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mtd><mtd style="padding-bottom: 0.5em;" class="mwe-math-columnalign-r"><mo stretchy="false">=</mo><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mi>k</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"><mi>K</mi><mi>cot</mi><mo>&#x2061;</mo><mi>K</mi><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">=</mo><mi>cot</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>k</mi><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mtd><mtd class="mwe-math-columnalign-r"><mo stretchy="false">=</mo><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">−</mo><mi>a</mi><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo stretchy="false">≪</mo><mi>K</mi></mrow></mrow></munder></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$A_{1}$

$K$

$r_{0}$

$A_{2}$

$k$

$r_{0}$

$δ_{0}$

$A_{2}$

$k$

$r_{0}$

$a$

$K$

$A_{1}$

$K$

$r_{0}$

$k$

$A_{2}$

$k$

$r_{0}$

$δ_{0}$

$A_{2}$

$k$

$e$

$m$

$K$

$K$

$r_{0}$

$k$

$r_{0}$

$δ_{0}$

$r_{0}$

$a$

$k$

$K$

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