(I have looked through 100 questions tagged quantum tunneling before asking)
I know how to calculate quantum tunneling for a single particle in a given potential energy landscape in single-particle quantum mechanics. My question is, can such a calculation be applied (roughly) to a particle passing through something as complicated as an ordinary brick wall (or stone, wood, metal, etc.), and if so, how do I estimate the potential height?
First suppose the tunneling particle is an electron. My first worry is that the wall is a many-electron (and nucleon) system so it is certainly wrong to imagine it as simply providing a potential barrier and nothing else, the way an electric field in vacuum would. But perhaps the concept of a simple potential barrier can be used to get an order of magnitude estimate? Is that right, or does Pauli exclusion and/or some complicated response of the material make it just wrong? (For a conductor, for example, you have image charges and things like that.) If the potential barrier model is of any use at all here, how do I estimate its height? (Anyone answering please feel free to invoke a crystalline solid, conducting if you like).
Secondly, I have the same question, but now for the case of a neutron. I think that in ordinary neutron diffraction and scattering experiments there is no need to invoke tunneling because the neutrons propagate in the ordinary way, but presumably at low enough energy they would not. What is the situation for an ordinary wall of some solid material such as brick, stone, etc?
If a meaningful rough answer can also be given for the de Broglie waves associated with the propagation of a neutral atom, then that would be an added bonus!