# A question about optical theorem

1. May 22, 2013

### ndung200790

Optical theorem says that total cross section proportion to elastic scattering amplitude in the forward direction.Then if the target is absolutely reflective ''mirror''(in the case of quantum mechanics:scattering potential=infinity(r<a) and de Broglie wave leng limits to 0),in this case the scattering amplitude in forward direction is zero,but the total cross section is nonzero (because of reflection).So I do not understand the optical theorem.

2. May 22, 2013

### DrDu

In wave optics the forward scattering amplitude is never zero. I.e. even behind some metallic mirror (in the distance of several hundred meters) a bright spot will appear in the shadow zone.
http://en.wikipedia.org/wiki/Arago_spot

Last edited: May 22, 2013
3. May 22, 2013

### ndung200790

And what about in the case of quantum mechanics?And in optics the thicker metalic mirror the smaller the total cross section?Because the thicker mirror the weaker the forward scattering.

4. May 22, 2013

### ndung200790

Now,I understand that it is not only because tunneling through barrier,but also because diffraction making the spot after mirror.

5. May 22, 2013

### ndung200790

But in case incident flux having diameter of the beam is very small comparision with diameter of the ''mirror'' and in classical limit(de Broglie wave leng tends to zero) and the momentum of particle is absolutely defined.So I think that having only reflection,but not having diffraction,then in this case there were not Arago spot?

6. May 22, 2013

### DrDu

I think the optical theorem refers to an incident plane wave. If the diameter of the incident beam is restricted, then you first have to decompose it in a plane wave basis.

7. May 22, 2013

### ndung200790

In case the diameter of mirror large enough(the region of scattering potential),then we can consider the incident flux is plane wave despite of the diameter of incident beam is narrower than that of mirror(and in classical limit).In this case,with unitary property of S matrix we deduce the optical theorem.Then we are led to the transfer amplitude allways exists,despite of the scattering potential limits to infinity?