Reduction of the Three Dimensional Schrodinger Equation for Multilayered Films

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.Comment: 14 pages, 1 figur

Democratic Capitalism and Philanthropy in a Global Economy

Democratic capitalism has become the popular paradigm in the modern world, and it is spreading further through globalization. It is a model based on growth, expansion and constant innovation. However, it is accompanied by social problems which may worsen despite overall gains in wealth. In this paper, we suggest that democratic capitalist societies may benefit from the application of what has been a primarily American institution: Philanthropy. We present the Entrepreneurship-Philanthropy Cycle, which demonstrates the relationship between wealthy entrepreneurs, philanthropic contributions and economic opportunity. As a nonmarket and nonstate mechanism, philanthropy is unique in its structure and operations, and may offer the ideal approach to solving social problems. We suggest that both the internationalization of American foundations, and the growth of domestic philanthropy, can help developing countries offset social problems