? Green's func for Helmholtz eqn

Hi:

Given a wave eqn, many books said that by assuming soln to be

of form u(t,x,y,z) = U(x,y,z)*exp( -i*w*t ) to obtain Helmholtz eqn.

Then Green's function of 3d Helmholtz eqn are G_ = exp( -i*k*r )/4/pi/r and

G+ = exp( i*k*r )/4/pi/r. Among them, G_ is going inward, and G+ is going

outward, and thus G+ is chosen as desired solution.

My question is, can we choose u(t,x,y,z) = U(x,y,z)*exp( i*w*t ) at the
very

begining. By doing that we still have the same Helmholtz eqn, but this time,

G_ is going outward, and G+ is going inward.

Then it seems that it does not matter to pick either G_ or G+ as Green's
func

of Helmholtz eqn. Both G_ or G+ can denote outgoing wave, depending on how

we choose the temperoal part. Is this true or only G_ or G+ can denote
outgoing

wave?

Thanks,
by Cheng Cosine
Jun/06/2k6 NC


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