In this paper we present a method for reducing the three dimensional Schrödinger equation to study confined metallic states, such as quantum well states, in a multilayer film geometry. While discussing some approximations that are employed when dealing with the three dimensionality of the problem, we derive a one dimensional equation suitable for studying such states using an envelope function approach. Some applications to the Cu/Co multilayer system with regard to spin tunneling/rotations and angle resolved photoemission experiments are discussed. Recent experimental studies of spin dependent, hot electron transmission such as those described in Ref. 4 and resonant tunneling through two discrete states (Ref. 5), have raised a number of interesting issues related to the ferromagnetic and insulating materials used, the nature of the electronic states that are involved in transmission and enhancements in spin filtering effects. Apart from the first principles based attempts which can be quite tedious, most theoretical studies of these spin dependent effects have used free electron band structures and other simplifications in the metallic as well as in the insulating regions. Our work, though motivated by free electron approaches such as those introduced by Slonczewski 6 , is an attempt to bring out a more realistic lateral dependence of the electronic states under consideration.This paper is organized as follows. First, starting from the three dimensional Schrödinger equation, we proceed to derive an envelope function approach suitable for multilayered films.This procedure will go beyond the free electron methods that have been commonly used in the past, making use of more realistic wave functions, but avoiding a full pledged ab-initio calculation when studying such systems. We introduce an approach which incorporates the two dimensional Bloch wave vector k || and show that the associated parallel band structure characteristic of the material being used, plays a major role in perpendicular transmission.Second, We will study spin tunneling and rotation effects (to be defined later) in a multilayer system with two ferromagnetic layers separated by a nonmagnetic metal such as Co/Cu/Co. We will also address some issues related to angle resolved photoemission and inverse photoemission experiments focused on confined states in metallic multilayers.

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