Reduction of the Three Dimensional Schrodinger Equation for Multilayered Films

TL;DR

This paper develops a method to simplify the three-dimensional Schrödinger equation into a one-dimensional form for analyzing quantum states in multilayer films, aiding studies of spin tunneling and photoemission.

Contribution

It introduces a novel envelope function approach to reduce the 3D Schrödinger equation for multilayer systems, enabling easier analysis of confined metallic states.

Findings

Derived a 1D equation for multilayer film states

Applied method to Cu/Co multilayers for spin analysis

Discussed approximations and their implications

Abstract

In this paper, we present a method for reducing the three dimensional Schrodinger 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 are discussed.