- #1
Spinnor
Gold Member
- 2,226
- 431
Suppose I have a pair of solutions of the one dimensional massless complex wave equation in 1+1 dimensional spacetime, solutions with equal and opposite momentum in some rest frame,
Ψ+ = exp[-i(Et+px)]
Ψ- = exp[-i(Et-px)]
Does it matter if
1) I sum Ψ+ and Ψ- and then preform a Lorentz Transformation, or
2) preform the Lorentz Transformation, L.T., on Ψ+ and Ψ- and then sum?
L. T. [f(x,t)+g(x,t)] = [L.T. f(x,t)]+[L.T. g(x,t)] ?
I think the answer is it should not matter the order of operation but I am having trouble simplifying my algebra. Just wondering if there is light at the end of the tunnel.
Thanks for any help!
Ψ+ = exp[-i(Et+px)]
Ψ- = exp[-i(Et-px)]
Does it matter if
1) I sum Ψ+ and Ψ- and then preform a Lorentz Transformation, or
2) preform the Lorentz Transformation, L.T., on Ψ+ and Ψ- and then sum?
L. T. [f(x,t)+g(x,t)] = [L.T. f(x,t)]+[L.T. g(x,t)] ?
I think the answer is it should not matter the order of operation but I am having trouble simplifying my algebra. Just wondering if there is light at the end of the tunnel.
Thanks for any help!