Interaction of two wavefunctions

In summary, the conversation discusses the possibility of computing optical coefficients of a material using only the wavefunctions of an incoming photon and a Bloch electron, along with the corresponding electronic density of states. The experts also mention the need for more advanced formalism, such as field theory or QED, to properly study the interaction between photons and Bloch electrons.
  • #1
Talker1500
22
0
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
 
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  • #2
Yes - you are scattering a photon off an electron in a solid.
 
  • #3
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 Schrodinger equation does not apply to them. More advanced formalism is needed (fields and field operators).
 
  • #4
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 schrodinger 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.
 

1. What is the significance of the interaction of two wavefunctions in quantum mechanics?

The interaction of two wavefunctions in quantum mechanics is significant because it allows us to understand and predict the behavior of particles at the microscopic level. When two wavefunctions overlap, the resulting interference pattern can tell us about the probability of finding a particle in a particular location.

2. How do two wavefunctions interact with each other?

The interaction of two wavefunctions is described by the principle of superposition, which states that when two or more waves overlap, the resulting wave is the sum of the individual waves. This means that the two wavefunctions will combine and interfere with each other, resulting in a new wavefunction.

3. What happens when two wavefunctions have the same frequency and amplitude?

If two wavefunctions have the same frequency and amplitude, they will interfere constructively, resulting in a larger amplitude and a more intense interference pattern. This is known as resonance and is commonly observed in physical systems such as musical instruments.

4. Can two wavefunctions cancel each other out?

Yes, two wavefunctions can cancel each other out if they have opposite phases. This is known as destructive interference and results in a decrease or complete cancellation of the amplitude of the resulting wavefunction.

5. Is the interaction of two wavefunctions always predictable?

No, the interaction of two wavefunctions can be unpredictable in certain situations, especially when dealing with complex systems. This is due to the non-linear nature of wave interactions and the fact that small changes in initial conditions can lead to significantly different outcomes.

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