EE1102 Quantum Physics Assignment Question | NTU

Assignment Instructions:  

• The assignment has 4 questions and is worth 100 marks in total
• Please show full, step-by-step working and reasoning to earn full credit 

The Compton shift equation is the shift in the photon wavelength after it scatters off an electron at rest. The photon in question, however, is in vacuum. In this assignment, we will explore the case where the incident and outgoing photons are in a non-vacuum medium.

In a medium of refractive index 𝑛, the wavelength of light 𝜆0 is related to its frequency 𝑓0 via the relation 𝜆0= 𝑐/(𝑛𝑓0) , where 𝑐 is the speed of light in  vacuum.  Fig. 1 is labelled with  variables of relevance, including input photon frequency 𝑓, outgoing photon angle 𝜃, outgoing photon frequency 𝑓′, outgoing electron angle 𝜙, outgoing electron energy 𝐸 and outgoing electron momentum 𝒑. In this problem, the momenta of all particles, before and after, lie entirely in the plane of the paper. 

1. Write the energy conservation equation and the momentum conservation equations for Compton scattering for incident and outgoing photons in a medium of  refractive index 𝑛. Explain your answer in detail.
2. Solve the equations to obtain the outgoing photon frequency 𝑓′ in the following form:
   
   
3. Show that your result in Question 2 is consistent with the Compton shift formula presented in lecture when 𝑛 = 1.
4. Let the percentage change in the photon energy be defined as
   

where  the  final  photon  energy  refers  is  being  collected  at  observation  angle 𝜃 = 180𝑜.  For incident light at photon energy 1 eV and in air (𝑛 = 1), what is the percentage change in the photon energy? How does this value change when silicon (𝑛 = 3.5) is used as the medium instead? You may assume that the observer is also in  the medium. Comment on how this  percentage change varied when we went from 𝑛 = 1 to 𝑛 = 3.5.