Exact solution to the behavior of the electron plasma in a metal layer in an alternating electric field

Exact expressions are obtained for the first time for the response of the conduction electrons in a metal layer to an external alternating electric field. Case's well-known method of separation of the variables is modified, and the methods of singular integral equations and boundary-value problems of complex analysis are used. The solutions can be used to determined the screened field and also the absorption in a metal layer in a wide range of frequencies.