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Display information for equation id:math.1819.29 on revision:1819
* Page found: Der nichtrelativistische Grenzfall (eq math.1819.29)
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TeX (original user input):
i\hbar {{\dot{\phi }}_{a}}=\left[ \frac{1}{2{{m}_{0}}}\left( {{{\bar{\pi }}}^{2}}+i\bar{\sigma }\left( \bar{\pi }\times \bar{\pi } \right) \right)+e\Phi \right]{{\phi }_{a}}=\left[ \frac{1}{2{{m}_{0}}}{{\left( \bar{p}-e\bar{A} \right)}^{2}}-\frac{1}{2{{m}_{0}}}e\hbar \bar{\sigma }\bar{B}+e\Phi \right]{{\phi }_{a}}
TeX (checked):
i\hbar {{\dot {\phi }}_{a}}=\left[{\frac {1}{2{{m}_{0}}}}\left({{\bar {\pi }}^{2}}+i{\bar {\sigma }}\left({\bar {\pi }}\times {\bar {\pi }}\right)\right)+e\Phi \right]{{\phi }_{a}}=\left[{\frac {1}{2{{m}_{0}}}}{{\left({\bar {p}}-e{\bar {A}}\right)}^{2}}-{\frac {1}{2{{m}_{0}}}}e\hbar {\bar {\sigma }}{\bar {B}}+e\Phi \right]{{\phi }_{a}}
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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"><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>π</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>i</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>π</mi><mo>¯</mo></mover></mrow></mrow><mo>×</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>π</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mi>e</mi><mi mathvariant="normal">Φ</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>−</mo><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mi>e</mi><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mi>e</mi><mi mathvariant="normal">Φ</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub></mstyle></mrow></math>
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