How Do Electron Transitions Correspond to Energy Levels in Quantum Wells?

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Homework Statement
Can someone check whether I've done the problems in the pictures properly? not sure if i've done them correctly.
Relevant Equations
n^2h^2/8(m_e)a^2
Screen Shot 2023-10-09 at 22.18.32.png
Screen Shot 2023-10-09 at 22.19.23.png
Screen Shot 2023-10-09 at 22.19.28.png

For the problem with the diagram, I'm getting from n=4 to n=2, n=5 to n=4, n=5 to n=1 and n=4 to n=1. n=4 to n=2 corresponds to n=1 to n=2 in well C; n=5 to n=4 corresponds to n=1 to n=2 in well D; n=5 to n=1 corresponds to n=1 to n=3 in well D and n=4 to n=1 corresponds to n=1 to n=2 in well E.
For the second problem, since the node separation is given by L/n where n is the state, and given that there is no nodes between 60pm and 80pm, i worked out that n=10. So the difference in energy is (10^2-9^2)h^2/(8(m_e)(300pm))?
 
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  • #2
sss1 said:
For the problem with the diagram, I'm getting from n=4 to n=2, n=5 to n=4, n=5 to n=1 and n=4 to n=1. n=4 to n=2 corresponds to n=1 to n=2 in well C; n=5 to n=4 corresponds to n=1 to n=2 in well D; n=5 to n=1 corresponds to n=1 to n=3 in well D and n=4 to n=1 corresponds to n=1 to n=2 in well E.
For the second problem, since the node separation is given by L/n where n is the state, and given that there is no nodes between 60pm and 80pm, i worked out that n=10. So the difference in energy is (10^2-9^2)h^2/(8(m_e)(300pm))?
That appears correct, except the denominator in the energy at the end.
 
  • #3
DrClaude said:
That appears correct, except the denominator in the energy at the end.
Needs squaring?
 
  • #4
sss1 said:
Needs squaring?
Yes, and why 300 pm?
 
  • #5
DrClaude said:
Yes, and why 300 pm?
Oh right, misread it. 200pm?
 
  • #6
sss1 said:
Oh right, misread it. 200pm?
Yes
 

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