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相対論 (1)  - 定数、換算式 -
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定数
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.. csv-table:: 
   :header: "constant", "value", "unit"
   :widths: 10, 10, 10

   "u", "931.4941", "(MeV)"
   "c", "2.99792458e8", "(m/s)"
   "e", "1.60217663e-19", "(C)"

   

換算式
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全エネルギー
----------------------

.. math::

   E &= m c^2 \\
     &= \gamma m_0c^2 \\
     &= \frac{m_0c^2}{\sqrt{1 - \beta^2}} \\

.. math::
   E &= E_0 + E_k \\
     &= m_0 c^2 + E_k

.. math::

   E = \sqrt{p^2 c^2 + m_0^2 c^4}

   
運動エネルギー
----------------------

.. math::

   E_k &= m_0c^2 (\gamma - 1) \\
       &= m_0c^2 \left( \frac{1}{\sqrt{1 - \beta^2}} - 1 \right)

.. math::

   E_k &= E - E_0 \\
       &= E - m_0 c^2

   
運動量
---------------
   
.. math::

   p = m_0c \gamma \beta

.. math::

   p = \frac{m_0c \beta}{\sqrt{1 - \beta^2}}

.. math::

   p = m_0c \sqrt{\gamma^2 - 1}

   
.. math::

   pc = E \beta

.. math::

   pc = \sqrt{E^2 - m_0^2 c^4}

.. math::

   pc = \sqrt{K^2 + 2Km_0c^2}


   
β、γの算出
---------------

.. math::

   \beta = \frac{\sqrt{K^2 + 2Km_0c^2}}{K + m_0c^2}
         = \frac{\sqrt{\left( \frac{K}{m_0c^2} \right)^2 + 2 \frac{K}{m_0c^2}}}{\frac{K}{m_0c^2} + 1}

.. math::

   \beta = \sqrt{1 - \left( \frac{m_0c^2}{E} \right)^2 }

.. math::

   \beta = \sqrt{1 - \frac{1}{\gamma^2}} = \frac{\sqrt{\gamma^2 - 1}}{\gamma}

.. math::

   \beta = \frac{\gamma\beta}{\sqrt{1 + (\gamma\beta)^2}}


   
.. math::

   \gamma = \frac{K}{m_0c^2} + 1

.. math::

   \gamma = \frac{E}{m_0c^2}

.. math::

   \gamma = \sqrt{1 + (\gamma\beta)^2}


   
.. math::

   \gamma\beta = \sqrt{\gamma^2 - 1}

.. math::

   \gamma\beta = \frac{\beta}{\sqrt{1 - \beta^2}}



参考文献
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* Physics Memo : Koba-wiki ( https://www.rcnp.osaka-u.ac.jp/~kobayash/be_koba/cgi-bin/moin.cgi/Physics%20Memo.html )