A Very Simple Quantum Mechanical Model for the Calculation of the Surface Free Energy and Surface Stress of Solids

For a model like that of Tamm, a linear periodical arrangement of a limited number of potential thresholds and wells is considered which is bordered by two higher potential steps at the ends representing the surfaces. Supposing the potential energy of the electrons in a solid is the sum of three functions each of which depends only on one of the co-ordinates x, y and z, the Schrodinger Equation is separable and a model for a three-dimensional solid can be assembled easily by the one-dimensional sub-systems. By adding the contributions of the electron states in the one-dimensional sub-systems, the surface energy and the surface stress have been calculated for a three-dimensional body.