Talk:Threshold energy

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There's an easier way to derive this. Using Lorentz invariance of the square of the total four-momentum along with conservation of momentum, we have $p_{\mathrm {tot} ,i}^{2}=p_{\mathrm {tot} ,f,cm}^{2}$ . Plugging in the threshold values for the final 4-momentum in the CM frame (rest mass energies, zero total momentum), and the energy equation $E_{1}^{2}=m_{1}^{2}+{\vec {p}}_{1}^{2}$ , the momentum terms cancel and we are left with the equation for $E_{1}$ . --Babomancer (talk) 02:10, 12 December 2014 (UTC)[reply]