Quesuion 3 (Marks 20) A particle with an energy Eis tunneling through a potential barrier (see figure below). Note that such a tunneling process takes place for example at a metal-Insulator-semiconductor thin film structure used in semiconducting industry. E E/2 2 (a) Sketch the form of the wavefunction expected In each of the 3 regions and give the functional forms of these wavefunctions. It is not required to give the precise mathematical expression of the final wavefunctions but the type of the waves. Explain the choice of the wavefunction for each region In a few words. [b) What are the mathematical boundary conditions for the waves when the particle enters and leaves the barrier? [c) Derive the equations that must be solved to obtain the constants appearing In the wavefunctions ( do not actually solve for them) . (d) If the potential energy In Region 3 Is exactly E/2, calculate the ratio of the wavelength in Regions 1 and 3