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May "Quantum tunneling" be wrong and an unnecessary term which should be deleted in later education of quantum mechanics?

+ 1 like - 1 dislike
85 views

In https://yourtimetravelexperience.com/quantum-tunneling-explained

First of all, any object is described by wavefunction in quantum mechanics. It just implies there is certain probability to find the say particle outside a potential well. However, the term "quantum tunneling" implies

1. An object travels from one point to another. 

2. Even if we do a measurement and we find it outside a potential well, it may be just originally there. However, the term tunneling implies it is originally at some point.

3. "Tunneling through a potential well" already implies an object is on one side of the potential well, and move to the other side. This is wrong.

All in all, may "Quantum tunneling" be an unnecessary term which should be deleted in later education of quantum mechanics?

asked May 16 in Chat by phi (20 points) [ revision history ]
recategorized May 16 by Dilaton

But this is exactly what happens: you have a beam of particles of well known properties and you scatter it off a barrier it should not be able to penetrate from a classical computation. And it does. I don't know what else would be enough for you to call "tunnelling".
 

disagree. You can find them at the other end. But you cannot say they go through the well.

Strictly speaking you are right, as in quantum mechanics it is not meaningful to talk about the state of the system before the measurement. So the notion of tunneling is just an interpretational visualision to help people imagine the situation but it is not physically and dynamically acurate.

Well, but it is meaningful to talk about the wave-function and this can be reconstructed from studying the beam exactly. In scattering, your wave-function has asymptotics defining the asymptotic momentum and energy. I.e., you can very well tell that this and this beam has this and this momentum and energy without collapsing the wave function. (A different point of view is that you collapse the wave function and measure the momentum/energy at infinity. You then let the collapsed, but fully valid wave scatter on your potential.) If a classical outcome is forbidden based on this momentum and energy but happens in the quantum case, this is very well defined tunneling.

Also, you can say that the particle does come through the barrier - there is a non-zero probability to find it in the "forbidden" region, it is just exponentially suppressed as you go away from the boundary of the "allowed" region.

I recommend considering explicit mathematical solutions of tunneling such as 1D scattering by a step potential before making such grand statements

understand, but this is static. After you find the particle, it is either in forbidden or allowed region. And it is stuck. There is no dynamics. So you cannot have the public image of a man passing through a wall due to quantum tunneling or the quantum mechanics path as in the picture above.

1 Answer

+ 2 like - 0 dislike

The term "quantum tunneling" implies (by definition) nothing less or more than ''given a particle inside a potential well at time $t$ there is a positive probability to find the same particle outside a potential well at a later time $t'$''.

The words used for this fact is just supposed to be an imaginative picture, like always when using semiclassical imagery for quantum events. Taking it literally is over-interpreting this imagery.

Therefore, arguing against the use of this language is moot. (Even in ordinary language, many terms are meaningless when taken literally.)

answered May 17 by Arnold Neumaier (12,385 points) [ revision history ]

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