
#1
Feb1514, 07:29 AM

P: 10

Hi everybody,
In most classical or quantum optics texts an angular momentum is considered for the EM radiation as the following: [itex] J = ε_0 ∫_V r × [E(r, t) × B(r, t)] d^3 r [/itex] Then it is claimed that: "Using the usual formula for a double vector product and integrating by parts, bearing in mind the assumption that the fields are zero at the surface of volume V introduced for the mode expansion, one finds that JR can be written as a sum of two terms: [itex]J = L + S , [/itex] given by [itex]L = ε_0 ∑_{j=(x,y,z)} ∫d^3r Ej (r, t)(r × ∇)Aj (r, t) ,[/itex] [itex]S = ε_0 ∫d^3r E(r, t) × A(r, t) [/itex] " Would you please help me derive them? Thank you 


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