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Display information for equation id:math.1605.43 on revision:1605
* Page found: Eigenschaften eindimensionaler stationärer Zustände (eq math.1605.43)
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Hash: bb02524209716d98763cde37e9875fc8
TeX (original user input):
0=\frac{d{{x}_{0}}}{dE}=-\frac{z({{x}_{0}})}{{{\phi }_{E}}\acute{\ }({{x}_{0}})}=-z{{({{x}_{0}})}^{2}}{{\left[ \int\limits_{-\infty }^{{{x}_{0}}}{{{\phi }_{E}}^{2}dx} \right]}^{-1}}<0
TeX (checked):
0={\frac {d{{x}_{0}}}{dE}}=-{\frac {z({{x}_{0}})}{{{\phi }_{E}}{\acute {\ }}({{x}_{0}})}}=-z{{({{x}_{0}})}^{2}}{{\left[\int \limits _{-\infty }^{{x}_{0}}{{{\phi }_{E}}^{2}dx}\right]}^{-1}}<0
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>0</mn><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>E</mi></mrow></mrow></mfrac></mrow><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><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></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></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><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mrow></mrow></mfrac></mrow><mo>=</mo><mo>−</mo><mi>z</mi><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</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></munderover><mrow data-mjx-texclass="ORD"><msup><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mo><</mo><mn>0</mn></mstyle></mrow></math>
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