The free space Lagrangian for a particle moving in 1D is L (x,x, t) = a) Show that pat = SL = ymv b) Now show that the Hamiltonian H(x, à, t) = x ³¹ – L(x, x, t) is ymc². - c) Now show that L = mc². where x¹ = (ct, x) dra dr dt -mc² 7 -naß dt
The free space Lagrangian for a particle moving in 1D is L (x,x, t) = a) Show that pat = SL = ymv b) Now show that the Hamiltonian H(x, à, t) = x ³¹ – L(x, x, t) is ymc². - c) Now show that L = mc². where x¹ = (ct, x) dra dr dt -mc² 7 -naß dt
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Transcribed Image Text:The free space Lagrangian for a particle moving in 1D is L (x,x, t)
=
a) Show that pat =
SL
=
ymv
b) Now show that the Hamiltonian H(x, à, t) = x ³¹ – L(x, x, t) is ymc².
-
c) Now show that L = mc².
where x¹ = (ct, x)
dra dr
dt
-mc²
7
-naß dt
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