Potential Step where E>V0. λ(II) always twice λ?

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In the discussion, the focus is on a particle approaching a potential step where the energy (E) exceeds the potential height (V0). The user observes that the characteristic wavelength (λ) in region II is consistently twice that of region I across multiple problems. This raises a question about whether this relationship is inherent to such scenarios. The user speculates that if E is significantly greater than V, the differences in wavelengths should be negligible, while if E is close to V, reflection occurs. The inquiry suggests a deeper exploration of the mathematical relationships governing wavefunctions in quantum mechanics.
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Homework Statement



I have been attempting some questions on a particle approaching a potential step where

E>V0

I have the provided solutions for all the questions and I noticed that λ(II) is always twice the value of λ in all the questions.

Is there some inherent reason for this, and is it always the case with this type of problem?

Thank you.


Homework Equations





The Attempt at a Solution

 
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What type of problem?

Assuming I and II are the regions before and after the step respectively, and λ is a characteristic wavelength of the wavefunction, so that k=2π/λ

If E >> V, the height of the step, then there should be almost no difference.
If E ~ V, then there should be some reflection off the edge of the step.

http://en.wikipedia.org/wiki/Soluti...nergy_greater_than_step_height_.28E_.3E_V0.29

Perhaps the problem was set up numerically so that E=(4/3)V or something?
 

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