Potential Step (wave amplitude)

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The discussion focuses on the behavior of wave amplitude in quantum mechanics when an incident wave approaches a potential step, specifically when the electron energy equals the potential energy V0. It is established that a free electron cannot possess a single energy value due to its distribution, leading to partial transmission and reflection of the wave. Additionally, the wavevectors on either side of the potential step differ, and there exists a specific energy level where the magnitudes of these wavevectors are equal, resulting in a 50% transmission and reflection ratio.

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solas99
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1. If the incident wave is coming from LHS,
what happens to the wave amplitude on the RHS when electron energy is equal V0?

2. the wavevectors on both sides of the step are different (generally), is there an energy at which the have the same magnitude?

thanks for any help..
 
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solas99 said:
1. If the incident wave is coming from LHS,
what happens to the wave amplitude on the RHS when electron energy is equal V0?
The usual way to analyse this problem uses assumptions about the electrons which cannot be satisfied in reality (especially: electrons with a single, fixed energy). And here you have a case where you can see this flaw.
If you have a free electron which "moves", it cannot have a single energy value, it has some distribution. The parts above V0 can (partially) go through, the other parts are reflected. If your electron does not "move", the question is ill-defined.

2. the wavevectors on both sides of the step are different (generally), is there an energy at which the have the same magnitude?
With low energy, everything gets reflected, with high energy, nearly everything is transmitted. So somewhere in between, you have 1/2 on both sides.
 

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