Experiments are proposed to study the properties of two-dimensional arrays of electrons on a helium surface with the purpose of better understanding the physics of particles confined to two-dimensions, to test new theories, and to use the special properties of the electron array as a model system to study analogs of three- dimensional systems. These include weakly-pinned charge-density waves and polarons. Particular emphasis will be placed on experiments designed to probe the quantum regime. The nature of quantum melting is of prime interest, and the phase diagram of electrons and its dependence on magnetic field will be studied. Electrons on helium films have a distinct advantage as a model system to study polarons and the conduction properties of weakly- pinned charge-density waves because the appropriate coupling parameter can be varied from the weak to strong limits by varying the film thickness, and the range from classical to the quantum limit can be spanned.
