External forces outside of a layered electron gas

We calculate the external forces outside of the surface of a layered electron gas (LEG). The LEG is a model of a metal where the electrical current is carried in parallel layers, and there is no current between layers. It describes the high-temperature cuprate superconductors and many other layered solids. We calculate the image potential from an external charge, the van der Waals potential from a neutral atom and the Casimir force between the parallel surfaces of two LEGs. Our theory does not use dielectric functions. We write down the quantum mechanical Hamiltonian, calculate the exact ground state energy and deduce the forces from the energy. We also show that the LEG has no surface plasmon.