E 1 + E 2 = m 0 c 2 E_1+E_2=m_0c^2 E 1 + E 2 = m 0 c 2
p 1 → + p 2 → = 0 \overrightarrow{p_1}+\overrightarrow{p_2}=0 p 1 + p 2 = 0
E 1 2 = m 1 2 c 4 E_1^2=m_1^2c^4 E 1 2 = m 1 2 c 4 and p 1 2 = 2 m 1 E 1 p_1^2=2m_1E_1 p 1 2 = 2 m 1 E 1
( m 0 c 2 − E 1 ) 2 = E 2 2 (m_0c^2-E_1)^2=E_2^2 ( m 0 c 2 − E 1 ) 2 = E 2 2
( m 0 c 2 − E 1 ) 2 = (m_0c^2-E_1)^2= ( m 0 c 2 − E 1 ) 2 =
= ( m 0 2 c 4 + m 1 2 c 4 − 2 m 0 c 2 m 1 c 2 ) = =(m_0^2c^4+m_1^2c^4-2m_0c^2m_1c^2)= = ( m 0 2 c 4 + m 1 2 c 4 − 2 m 0 c 2 m 1 c 2 ) =
= c 4 ( m 0 2 + m 1 2 − 2 m 0 m 1 ) = =c^4(m_0^2+m_1^2-2m_0m_1)= = c 4 ( m 0 2 + m 1 2 − 2 m 0 m 1 ) =
= c 4 ( m 0 2 + m 1 2 ) − c 2 2 m 0 E 1 =c^4(m_0^2+m_1^2)-c^22m_0E_1 = c 4 ( m 0 2 + m 1 2 ) − c 2 2 m 0 E 1
E 2 2 = m 2 2 c 4 E_2^2=m_2^2c^4 E 2 2 = m 2 2 c 4
m 2 2 c 4 = c 4 ( m 0 2 + m 1 2 ) − c 2 2 m 0 E 1 → m 2 2 c 2 = c 2 ( m 0 2 + m 1 2 ) − 2 m 0 E 1 m_2^2c^4=c^4(m_0^2+m_1^2)-c^22m_0E_1\to m_2^2c^2=c^2(m_0^2+m_1^2)-2m_0E_1 m 2 2 c 4 = c 4 ( m 0 2 + m 1 2 ) − c 2 2 m 0 E 1 → m 2 2 c 2 = c 2 ( m 0 2 + m 1 2 ) − 2 m 0 E 1
So, we have
E 1 = c 2 2 m 0 ( m 0 2 + m 1 2 − m 2 2 ) E_1=\frac{c^2}{2m_0}(m_0^2+m_1^2-m_2^2) E 1 = 2 m 0 c 2 ( m 0 2 + m 1 2 − m 2 2 ) Answer.
Comments