Matter Waves & Electron Traps: Angular Momentum Explained

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SUMMARY

The discussion centers on the relationship between matter waves, electron traps, and angular momentum in quantum mechanics. The equation hf = ΔE = Ehigh - Elow illustrates how an electron in a one-dimensional infinite potential well absorbs a photon, where hf represents the photon's energy. However, the application of this equation to real electron traps is limited due to the conservation of angular momentum, which is not defined in one-dimensional systems. The inability to apply these principles to unreal electron traps highlights the importance of angular momentum in photon interactions.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the concept of matter waves
  • Knowledge of photon absorption and emission processes
  • Basic grasp of angular momentum in physics
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  • Study the implications of angular momentum conservation in quantum mechanics
  • Explore the differences between real and unreal electron traps
  • Learn about the role of matter waves in quantum systems
  • Investigate the mathematical derivation of the equation hf = ΔE
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Students and researchers in physics, particularly those focusing on quantum mechanics, matter waves, and the behavior of electrons in potential wells.

emperrotta
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I am currently reading about matter waves and electron traps.

the textbook states, by the equation:

hf = \DeltaE = Ehigh - Elow

If an electron confined to a one-dimensional infinite potential well is to absorb a photon, the energy hf of the photon must equal the energy difference \DeltaE between the initial energy level of the electron and a higher level.

Then as an aside, the textbook states:
Although the above equation and what we have discussed about photon absorption and emission can be applied to physical (real) electron traps, they actually cannot be applied to one-dimensional (unreal) electron traps. The reason involves the need to conserve angular momentum in a photon absorption or emission process.

I do not understand this statement about angular momentum.
 
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It's because a photon carries angular momentum, but in 1-D the concept of angular momentum is not defined.
 

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