Can a single electron slide down a smooth glass incline plane?

I can understand why someone might ponder this. The key is to recognize that sliding is a classical phenomenon of macroscopic objects, and electrons belong to a completely different regime. So no, an electron cannot “slide” down a glass plane.

Glass is made of atoms held in a (more-or-less) rigid structure. These atoms have positively charged nuclei and negatively charged electron orbitals surrounding them. At the atomic scale, the electric potentials in a solid-state medium are enormously complex, especially for an amorphous material. Moreover, surfaces have the added complexity of dangling bonds and further defects.

If an electron is magically placed with no velocity in “contact” with an inclined glass plane, it will experience the complex electrical environment of the surface in addition to gravity. But also, it will itself distort the orbitals with which it interacts. Overall, the gravitational potential will be totally insignificant compared to the electrical potentials.

The only way one I could imagine anything remotely resembling sliding would be a for a completely contrived and unphysical situation, where the electrical forces just perfectly balance out such that the minuscule gravitational force would play a role. And furthermore, it wouldn’t be “sliding” but more like “hopping” from one lattice position to the next.