Homework 4 Due Tuesday, October 12 Learning Objective To Derive 3D Density of States and Density-of-States Effective Mass (a) Given a conduction band with parabolic E vs k and isotropic effective mass: A surface of constant energy in k space is therefore a sphere of radius Derive the expression for the density of states In a cube-shaped sample of dimensions LxLxL Hints: By using standing waves sin(kxx)sin(kyy)sin(kzz) you can restrict your attention to positive values of kx, ky and kz. Each state has a volume of p3/L3 in k space. So all the states with energy less than E occupy one octant of the above mentioned sphere. So the total number of states