I Can Quantum Tunneling Occur Through a Material Barrier?

[Swamp Thing]

A lot of popular level explanations introduce the idea of tunneling by saying that "in principle" a person in one room can "find themselves" in the next room, i.e. one can tunnel through a wall

Of course, the presenter then hastens to clarify that this is so unlikely that we would have to wait longer than the age of the universe in order to have some chance of witnessing a macroscopic tunneling event.

On the other hand, in physics texts we only see examples of tunneling where the barrier is an energy hill rather than a wall composed of atoms. The wavefunctipn has a non zero value beyond the potential barrier.

So my question is, is it at all possible for tunneling to happen through a material barrier? I'm thinking of, say, an atom or small molecule tunneling through a film that is one atom thick. (But assiming a scenario where classical diffusion would not occur). Would the wavefunction ooze through such a film?

 

[trurle]

A lot of popular level explanations introduce the idea of tunneling by saying that "in principle" a person in one room can "find themselves" in the next room, i.e. one can tunnel through a wall

Of course, the presenter then hastens to clarify that this is so unlikely that we would have to wait longer than the age of the universe in order to have some chance of witnessing a macroscopic tunneling event.

On the other hand, in physics texts we only see examples of tunneling where the barrier is an energy hill rather than a wall composed of atoms. The wavefunctipn has a non zero value beyond the potential barrier.

So my question is, is it at all possible for tunneling to happen through a material barrier? I'm thinking of, say, an atom or small molecule tunneling through a film that is one atom thick. Would the wavefunction ooze through such a film?

This effect (tunneling through thin stack of atoms) is known and even used in device called "tunnel diode".

 

[Swamp Thing]

Thanks for the prompt reply. I did think of the tunnel diode before posting, but I had the impression that the barrier at the junction is still a potential barrier from the view point of an electron. After all, an electron is pretty free to move through a conductor or a doped semiconductor, and it is only the junction potential profile that stops electrons from wandering across. In some sense, the junction barrier seems to lack the "solidity" of a wall. And a free electron is inherently a part of the solid state structure of the diode, so it doesn't seem very amazing that it can tunnel across the junction.

But after thinking about your post for a while, I did realize that any "solid" barrier works only because of electrostatic forces. Considering a mesoscopic example -- a very thin insulating polymer film and, say, a heavy ion or small molecule. In this case, a classical path through the barrier would involve intermediate stages where the molecule would feel strong electrostatic forces that would try to push it back -- places where the potential energy would be locally high.

So my distinction between the tunnel diode and a brick wall was probably an arbitrary one, so thank you again for the reply.

 

[Swamp Thing]

But there is still this nagging question in my mind. Are there examples where the wavefunction of a mesoscopic composite object passes through a large, thin, massive composite object, to an extent that it can show up as a measurable effect?

 

[PeterDonis]

in physics texts we only see examples of tunneling where the barrier is an energy hill rather than a wall composed of atoms

What do you think produces the "energy hill"?