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Display information for equation id:math.1605.35 on revision:1605

* Page found: Eigenschaften eindimensionaler stationärer Zustände (eq math.1605.35)

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TeX (original user input):

\begin{align}
& \left( {{\phi }_{E}}\acute{\ }z-{{\phi }_{E}}z\acute{\ } \right)\left. {} \right|_{-\infty }^{{{x}_{0}}}={{\phi }_{E}}\acute{\ }({{x}_{0}})z({{x}_{0}})-{{\phi }_{E}}({{x}_{0}})z\acute{\ }({{x}_{0}})-{{\phi }_{E}}\acute{\ }(-\infty )z(-\infty )+{{\phi }_{E}}(-\infty )z\acute{\ }(-\infty ) \\
& {{\phi }_{E}}({{x}_{0}})={{\phi }_{E}}\acute{\ }(-\infty )=0 \\
& \Rightarrow \left( {{\phi }_{E}}\acute{\ }z-{{\phi }_{E}}z\acute{\ } \right)\left. {} \right|_{-\infty }^{{{x}_{0}}}={{\phi }_{E}}\acute{\ }({{x}_{0}})z({{x}_{0}}) \\
\end{align}

TeX (checked):

{\begin{aligned}&\left({{\phi }_{E}}{\acute {\ }}z-{{\phi }_{E}}z{\acute {\ }}\right)\left.{}\right|_{-\infty }^{{x}_{0}}={{\phi }_{E}}{\acute {\ }}({{x}_{0}})z({{x}_{0}})-{{\phi }_{E}}({{x}_{0}})z{\acute {\ }}({{x}_{0}})-{{\phi }_{E}}{\acute {\ }}(-\infty )z(-\infty )+{{\phi }_{E}}(-\infty )z{\acute {\ }}(-\infty )\\&{{\phi }_{E}}({{x}_{0}})={{\phi }_{E}}{\acute {\ }}(-\infty )=0\\&\Rightarrow \left({{\phi }_{E}}{\acute {\ }}z-{{\phi }_{E}}z{\acute {\ }}\right)\left.{}\right|_{-\infty }^{{x}_{0}}={{\phi }_{E}}{\acute {\ }}({{x}_{0}})z({{x}_{0}})\\\end{aligned}}

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(ϕE ´zϕEz ´)|x0=ϕE ´(x0)z(x0)ϕE(x0)z ´(x0)ϕE ´()z()+ϕE()z ´()ϕE(x0)=ϕE ´()=0(ϕE ´zϕEz ´)|x0=ϕE ´(x0)z(x0)
<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"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>z</mi><mo stretchy="false"></mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mi>z</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false"></mo><mi mathvariant="normal"></mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></msubsup><mo stretchy="false">=</mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mi>z</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false"></mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mi>z</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false"></mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mo stretchy="false"></mo><mi mathvariant="normal"></mi><mo stretchy="false">)</mo><mi>z</mi><mo stretchy="false">(</mo><mo stretchy="false"></mo><mi mathvariant="normal"></mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mo stretchy="false">(</mo><mo stretchy="false"></mo><mi mathvariant="normal"></mi><mo stretchy="false">)</mo><mi>z</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mo stretchy="false"></mo><mi mathvariant="normal"></mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mo stretchy="false"></mo><mi mathvariant="normal"></mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false"></mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>z</mi><mo stretchy="false"></mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mi>z</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false"></mo><mi mathvariant="normal"></mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></msubsup><mo stretchy="false">=</mo><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mi>z</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

  • ϕE
  •  ´
  • z
  • ϕE
  • z
  •  ´
  • x0
  • ϕE
  •  ´
  • x0
  • z
  • x0
  • ϕE
  • x0
  • z
  •  ´
  • x0
  • ϕE
  •  ´
  • z
  • ϕE
  • z
  •  ´
  • ϕE
  • x0
  • ϕE
  •  ´
  • ϕE
  •  ´
  • z
  • ϕE
  • z
  •  ´
  • x0
  • ϕE
  •  ´
  • x0
  • z
  • x0

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