Practice Problem Set 2

1. Are the x-component of the angular momentum and kinetic energy compatible observables?
2. Show that is a kinetic energy eigenfunction. Relate the wavevector to the kinetic energy.
3. Tunneling imposes fundamental limits on the design of conventional microelectronic devices because electrons can jump between adjacent circuit elements and thus potentially change values stored in processors and memory chips. Microchips are made by laying down layers of conductive materials (``wires'') and semiconductors (transistors and other computing elements). Suppose that two wires come within of each other. (This separation is only slightly beyond the limits of current fabrication technology.) The insulating material between them provides a potential barrier of 4.5eV. The electrons in the wires have a kinetic energy of 3.3eV. ( .) What fraction of the current in one wire will appear in the other? How close together can the wires be if the tunneling probability is not to exceed one part in ?