The elastic displacement and stress in a material to promote reflection and transmission of an incoming wave

The conditions on elastic displacement and stress in a material that will promote reflection and transmission of an incoming wave are calculated. It is found, for example, that to optimize reflection and transmission, scalar potentials of the displacement in the wave and in the material will be related to rotations in planes perpendicular and parallel to the direction of propagation to the wave. When a pulse is constructed and its path analyzed through short distances, it is shown that abrupt transitions in tension and compression in a material will maximize reflection of the pulse. When strain energy is minimized where reflection and refraction are to occur, differences in tension and compression become prominent again. Finally, an approximate volume of material is calculated for an electron to harness the restoring forces in a material to balance the energy lost in inelastic scattering.