# Infinite potential barrier

#### dakold

I got a question about an infinite potential barrier. If a particle with a momentum p travell through an infinite potential barrier, how can the energy be conserved, thus how can the particle have the same momentum after passing the barrier? Does there exists any real life example?

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#### jtbell

Mentor
An infinitepotential barrier? If a barrier has infinite potential, the transmission probability is zero. Or to put it more precisely (since there really isn't any such thing as an infinite potential barrier), as the "height" of the barrier increases without limit, the transmission probability decreases asymptotically towards zero.

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

#### dakold

I’m think of a particle, with momentum p, that travels in a region there the potential is zero and comes to a place there it exist an infinte potential barrier and travels through the region and comes to a region there the potential is again zero. How can the particle after the barrier have the same momentum p?

#### ZapperZ

Staff Emeritus
2018 Award
I’m think of a particle, with momentum p, that travels in a region there the potential is zero and comes to a place there it exist an infinte potential barrier and travels through the region and comes to a region there the potential is again zero. How can the particle after the barrier have the same momentum p?
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.

#### dakold

Of course that can't be an infinite barrier. So the same particle as above, but the difference is that the potential is finite. How can the momentum be conserved?

#### ZapperZ

Staff Emeritus
2018 Award
Of course that can't be an infinite barrier. So the same particle as above, but the difference is that the potential is finite. How can the momentum be conserved?
OK, so now you are changing the scenario?

This is getting rather confusing.

Zz.

#### dakold

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?
If a particle, with momentum p, is travelling 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?

#### ZapperZ

Staff Emeritus
2018 Award
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 travelling 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 expected since it is interacting with an external field. You can easily say the same thing in the QM case.

Zz.

#### dakold

I understand how I can describe this in classic mechanic. So another question, where can I see this applicated in real life?

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