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

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In summary, electron transitions in quantum wells correspond to energy levels determined by the confinement of electrons in a potential well created by barriers. When an electron absorbs or emits energy, it can move between quantized energy states. These transitions result in the emission or absorption of photons, with energy differences between the levels corresponding to the photon's energy, thus linking quantum mechanics to observable optical phenomena. The discrete nature of these energy levels is a fundamental characteristic of quantum wells, impacting their applications in optoelectronics and semiconductor technology.
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sss1
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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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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
 

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

What is an electron transition in a quantum well?

An electron transition in a quantum well refers to the movement of an electron between different energy levels within the well. These transitions occur when an electron absorbs or emits a photon, causing it to jump from one quantized energy state to another.

How are energy levels in a quantum well determined?

Energy levels in a quantum well are determined by the quantum mechanical properties of particles confined in a potential well. The specific energy levels depend on the width and depth of the well, as well as the effective mass of the electron. These levels are quantized, meaning only specific energy states are allowed.

What role does the width of the quantum well play in electron transitions?

The width of the quantum well significantly affects the energy levels. A narrower well results in higher energy separation between levels because the electron is more confined. Conversely, a wider well leads to smaller energy differences between levels. This width-dependent behavior influences the wavelengths of photons absorbed or emitted during electron transitions.

How do selection rules affect electron transitions in quantum wells?

Selection rules dictate the allowed transitions between energy levels based on quantum mechanical principles, such as conservation of angular momentum. In quantum wells, these rules often restrict transitions to those where the change in the principal quantum number is ±1. This ensures that only specific transitions are permitted, influencing the optical properties of the material.

What experimental techniques are used to study electron transitions in quantum wells?

Several experimental techniques are used to study electron transitions in quantum wells, including photoluminescence spectroscopy, absorption spectroscopy, and photoreflectance. These methods involve shining light on the quantum well and measuring the emitted or absorbed photons, providing insights into the energy levels and transition dynamics.

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