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

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In summary, the conversation discusses questions on a particle approaching a potential step with energy greater than the potential, and the observation that the value of λ(II) is always twice that of λ in all the questions. The conversation also mentions some possible reasons for this and speculates on the numerical setup of the problem.
  • #1
ZedCar
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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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  • #2
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?
 

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

1. What is a potential step in physics?

A potential step is a sudden change in the potential energy of a particle, typically in the context of quantum mechanics. This change can occur in a variety of systems, such as a particle approaching a potential barrier or a particle moving between different potentials in a crystal lattice.

2. What does it mean when E > V0 in a potential step?

When E > V0 in a potential step, it means that the energy of the particle is greater than the potential energy of the barrier it is approaching. This indicates that the particle has enough energy to overcome the barrier and continue moving forward.

3. What is the significance of λ(II) being twice λ in a potential step?

In a potential step where E > V0, the particle has a non-zero probability of being transmitted through the barrier. The ratio of the transmitted probability amplitude to the incident probability amplitude is given by the transmission coefficient λ. In a potential step, the transmission coefficient λ is twice the incident coefficient, indicating that there is a higher likelihood of the particle being transmitted through the barrier rather than being reflected back.

4. How does the potential step behave when E < V0?

When E < V0 in a potential step, the particle does not have enough energy to overcome the potential barrier. This results in a higher likelihood of the particle being reflected back rather than being transmitted through the barrier.

5. What is the relationship between the energy of the particle and the potential barrier in a potential step?

The energy of the particle and the potential barrier in a potential step are directly related. If the energy of the particle is greater than the potential barrier, the particle has a higher probability of being transmitted through the barrier. If the energy is less than the potential barrier, the particle has a higher probability of being reflected back.

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