Interaction of two wavefunctions

[Talker1500]

Hi,

I've been thinking about the following scheme: let's say I have an incoming photon ray with wavefunction ψ₁ that finds a bloch electron with wavefunction ψ₂. Is there any way to compute the optical coefficients (transmitivity, reflectivity etc) of the material knowing only this two ψ and the corresponding electronic DOS due to the bloch electrons?

Thanks

 

[Simon Bridge]

Yes - you are scattering a photon off an electron in a solid.

 

[erst]

The wavefunction contains complete knowledge of the system, so I think yes it should be possible to compute all materials properties in principle.

But is it meaningful to talk of a photon wavefunction? The Schrödinger equation does not apply to them. More advanced formalism is needed (fields and field operators).

 

[Simon Bridge]

Pretty much - you will see treatments that talk about a plane-wave state for incoming photons etc. for the scattering regime ... i.e. we can certainly write down a Schrödinger equation for a system composed of matter and photons in Columb gauge.

But a proper QM treatment for the interaction of photons and Bloch electrons will involve field theory or, at least, QED.