Finite well penetration depths dependence on Well Length

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SUMMARY

The discussion centers on the relationship between well length (L) and energy levels in finite square wells. It establishes that as L decreases, energy increases, leading to a decrease in wavelength. However, the implications of wavelength on penetration depth are debated, with one participant suggesting that a smaller wavelength could lead to reduced penetration depth. A recommendation is made to work through the solution of the finite square well to clarify these relationships.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically wave functions.
  • Familiarity with finite square well models in quantum physics.
  • Knowledge of energy-wavelength relationships in quantum systems.
  • Basic mathematical skills for solving differential equations related to wave functions.
NEXT STEPS
  • Study the finite square well model in quantum mechanics.
  • Learn how to derive energy levels and wave functions for finite wells.
  • Explore the concept of penetration depth in quantum mechanics.
  • Investigate the mathematical relationship between wavelength and energy in quantum systems.
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics and wave function analysis, will benefit from this discussion.

PsychonautQQ
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So in the infinite well Energy is proportional to 1/L^2, so I'm assuming in the finite well there is some sort of similar relation. So as the L decreases, the energy increases, so the wavelength decreases. Decreasing the wavelength means more energy, so it should penetrate further, but also if you draw the situation a smaller wavelength will make it penetrate less far, although the well also is getting smaller so blahh I'm trying to figure out how all this adds up. Thanks!
 
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PsychonautQQ said:
but also if you draw the situation a smaller wavelength will make it penetrate less far

What do you mean by this? I don't think it's correct.

I suggest you actually work through the solution of the finite square well and see how the penetration length of the ground state wave function depends on L.
 

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