Section 9.2: Exploring Classical and Quantum Scattering

select, then click a link below to see the classical electromagnetic wave.

select,  then click a link below to see the sum of the classical electromagnetic waves.

select, then click a link below to see quantum-mechanical plane wave.

n1 = V1= 1 n2 or V2 = 1 n2 or V2 = 2 n2 or V2 = 3 n2 or V2 = 4 n2 or V2 = 5
n2 = V2 = 1 n1 or V1 = 1 n1 or V1 = 2 n1 or V1 = 3 n1 or V1 = 4 n1 or V1 = 5

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This Exploration stresses the similarities and differences between a classical electromagnetic wave incident on a change (an increase or decrease) of index of refraction and a quantum-mechanical plane wave incident on a change (an increase or decrease) in potential energy. Use the check boxes to switch between classical and quantum-mechanical waves to see the result of the sum of the incident and reflected electromagnetic waves in Region I.  Restart.

Answer the following questions for both the case of  n1 < n2 and n1 > n2  and V1 < V2 and V1 > V2.

  1. What is the phase of the reflected wave relative to the incident wave in the classical and quantum-mechanical cases?
  2. What happens to the amplitude of the wave in Region II for the classical and quantum-mechanical cases?
  3. As n2 >> n1 and as V2 >> V1, what does the superposition of the incident and reflected waves look like in the classical and quantum-mechanical cases?
  4. What happens to the wavelength and speed of the electromagnetic wave in Region II as compared to Region I?  What happens to the curviness and the momentum of the quantum-mechanical plane wave in Region II as compared to Region I?

Note that the quantum-mechanical case is considered in detail beginning in Section 9.4.

 

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