Can a particle / wave pass through a sheet of material?

[MikeeMiracle]

TL;DR Summary

Can a particle / wave pass through a sheet

I have heard that if you could make a sheet of material thinner than a wavelength representing a particle and fire particles at it, that particle might be detected on the other side of the sheet material when you try and detect it due to Quantum Tunneling i believe.

Does that mean that it's just been detected there once or can it actively carry on moving past the sheet once it has appeared on the other side?

Thanks

 

[Drakkith]

Does that mean that it's just been detected there once or can it actively carry on moving past the sheet once it has appeared on the other side?

Yes, it can carry on moving past the sheet after detection as long as your experimental setup allows it.

 

[vanhees71]

Well, as learned by Rutherford in his famous gold-foil experiment, it's no problem for particles (in this case ##\alpha## particles from some radioactive substance) to just go through the foil. This has nothing to do with tunneling but with the fact that matter is pretty "empty". It consists of small atomic nuclei (typical scales are some fm, i.e., some ##10^{-15} \text{m}##) around which the electons are grouped in pretty large distances (typical scale is the Bohr radius of a hydrogen atom which is about ##5 \cdot 10^{-11} \; \text{m}##. Only a few ##\alpha## particles got scattered due to the Coulomb force between nuclei and the ##\alpha## particles. This was in fact the discovery of the atomic nucleus and the beginning of modern atomic physics.

 

[Nugatory]

Does that mean that it's just been detected there once or can it actively carry on moving past the sheet once it has appeared on the other side?

Once it's been detected at any location, we use Schrodinger's equation to calculate the future evolution of its state starting from the initial condition "At time T it was right here where where our detector triggered at that time". The math-free layman's summary of this calculation is that you can think of it as actively carrying on moving past the sheet.

Note that this isn't all that different than what we did at the beginning to calculate the tunneling probability: We used Schrodinger's equation to calculate the future evolution the particle state; the difference is that we we started from the initial condition "it is moving towards the barrier with momentum p".

 

[Nugatory]

I have heard that if you could make a sheet of material thinner than a wavelength representing a particle and fire particles at it, that particle might be detected on the other side of the sheet material when you try and detect it due to Quantum Tunneling i believe.

In most intro QM courses, tunnelling is introduced by solving Schrodinger's equation for a particle with energy ##E## when the potential ##V(x)## is zero everywhere except between ##x=0## and ##x=A##, where it is ##V_0>E##. That corresponds to a barrier of thickness ##A##.

The tunneling probaility drops off as the thickness of the barrier increases, but there's no hard cutoff at one wavelength. The wave function declines exponentially in the range beween ##x=0## and ##x=A## but it never goes all the way to zero.

This idealized setup is a good start for understanding most problems in which tunneling is relevant, but it turns out to be a poor description of the specific setup you're describing, where the barrier is a sheet of material only a few wavelengths thick. The problem is that at this scale we cannot ignore the atomic structure of the material making up the barrier. For most physically reasonable configurations ##V_0## is less than ##E## and the particle gets to the other side, but not because of tunneling - it gets through the barrier the same way an armor-piercing shell gets through a sheet of armor plate.