Cairo University Modern Physics Sheet 5 PDF

Cairo University Faculty of Engineering Credit Hours System Modern Physics Sheet_5 The Schrödinger Equation 2 -31 me = 9.1 x 10 k...

Cairo University Faculty of Engineering Credit Hours System Modern Physics Sheet_5 The Schrödinger Equation 2 -31 me = 9.1 x 10 kg e = 1.6 x 10-19 C ħ = 1.05 x 10-34 J.s (1) (i)Write down the 1-D time independent Schrödinger equation in each region of the following potential energy diagrams for an electron with total energy E. (ii) Find the general solution ψ(x) in each region (iii ) Apply the boundary conditions (iv) Find relations between the constants of the general solutions ∞ E Uo Uo Uo E x 0 L x 0 L (a) (b) (2) A beam of particles of energy E are incident from left upon a potential step of Uo =3/4 E at x=0. The wavefunction of such incident particles is: ψinc(x) = eikx (a) Write the general solution in all regions. (b) Calculate the reflectance, R and the transmittance, T. (3) Find a general solution, ψ(x), for an electron with total energy E = 0.5eV as shown in the figure below. Find the numerical values of “k” and “”. U(x) U=1 eV E=0.5 eV x 0 U=-0.5 eV