Density of States for Ballistic Electrons in Electric and Magnetic Fields

The density of states for ballistic electrons in the presence of an electric field of almost arbitrary shape is calculated for one, two, and three dimensions using the semiclassical quantization in a finite sample. The semiclassical results are compared with these of the complete quantum treatment for a constant electric field. The case of crossed electric and magnetic fields is also considered and it is demonstrated that in this configuration the density of states exhibits a transition between magnetic and electric types of motion. Implications of this transition for the quantum Hall effect are mentioned.