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dakold

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- Thread starter dakold
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- #1

dakold

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- #2

jtbell

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Can you give a specific example of the kind of situation you're thinking of?

- #3

dakold

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- #4

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Off the top of my head, the ONLY "infinite" potential barrier that allows a transmission is a delta function barrier. All other infinite barrier with a finite width will cause the wavefunction to be identically zero at the boundary, so no transmission!

So, do you want to rephrase your question?

Zz.

- #5

dakold

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- #6

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OK, so now you are changing the scenario?

This is getting rather confusing.

Zz.

- #7

dakold

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If a particle, with momentum p, is traveling in a region with the potential is equal to zero, at some place the potential is not zero, if my thought above is correct than shall the potential be finite. After that the potential is again zero, is the momentum conserved?

- #8

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I understand that I have confused you. My thought was that I must have misunderstands something because of the explanations that stated above. The case that I did think of was an infinite potential barrier with a width, but if the wavefunction is zero at the boundary than the momentum can’t be conserved, or I’m a wrong? So if the momentum shall be conserved it most be a finite barrier, or?

You are wrong. You are forgetting that (i) this implies a reflection at the boundary and (ii) any change in momentum is due to the interaction with the potential barrier. This is no different than a classical ball-bounce-off-wall scenario!

If a particle, with momentum p, is traveling in a region with the potential is equal to zero, at some place the potential is not zero, if my thought above is correct than shall the potential be finite. After that the potential is again zero, is the momentum conserved?

Sure it is! This is because the potential field INTERACTS on the particle!

From the way you are describing this difficulty, you may want to go back and look at your classical mechanics again. I can reformulate everything you said here in terms of classical mechanics with a classical particle going into a potential field. Any change in momentum here can be entirely explained by the interaction of that particle with such a field. A comet from far away coming into the gravitational potential of a celestial body and changes its momentum. Do you see any problem in this case? That change is to be

Zz.

- #9

dakold

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