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Display information for equation id:math.1816.61 on revision:1816

* Page found: Klein- Gordon- Gleichung (eq math.1816.61)

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TeX (original user input):

E=\pm {{m}_{0}}{{c}^{2}}\sqrt{\left[1+{{\left( \frac{\hbar \bar{k}}{{{m}_{0}}c} \right)}^{2}} \right]}\approx \pm {{m}_{0}}{{c}^{2}}\left[1+\frac{1}{2}{{\left( \frac{\hbar \bar{k}}{{{m}_{0}}c} \right)}^{2}} \right]=\pm \left[{{m}_{0}}{{c}^{2}}+{{\frac{\left( \hbar \bar{k} \right)}{2{{m}_{0}}}}^{2}} \right]

TeX (checked):

E=\pm {{m}_{0}}{{c}^{2}}{\sqrt {\left[1+{{\left({\frac {\hbar {\bar {k}}}{{{m}_{0}}c}}\right)}^{2}}\right]}}\approx \pm {{m}_{0}}{{c}^{2}}\left[1+{\frac {1}{2}}{{\left({\frac {\hbar {\bar {k}}}{{{m}_{0}}c}}\right)}^{2}}\right]=\pm \left[{{m}_{0}}{{c}^{2}}+{{\frac {\left(\hbar {\bar {k}}\right)}{2{{m}_{0}}}}^{2}}\right]

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E=±m0c2[1+(k¯m0c)2]±m0c2[1+12(k¯m0c)2]=±[m0c2+(k¯)2m02]
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>E</mi><mo>=</mo><mo>&#x00B1;</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow></msqrt></mrow><mo>&#x2248;</mo><mo>&#x00B1;</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><mo>&#x00B1;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></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="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Klein- Gordon- Gleichung page

Identifiers

  • E
  • m0
  • c
  • k¯
  • m0
  • c
  • m0
  • c
  • k¯
  • m0
  • c
  • m0
  • c
  • k¯
  • m0

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