V(x) = { 10 eV, x < 0, 0, x > 0. (a) (5 pts) Write the time-independent Schro?dinger equation in the regions x < 0 and x > 0. (b) (5 pts) An electron with a kinetic energy of 15 eV is moving from left to right in this potential. Write down the boundary conditions at x = 0. (c) (10 pts) From (b), solve the wave function ?(x) for regions x < 0 and x > 0. (d) (10 pts) From (b), calculate the probability that the electron will (i) continue moving along its initial direction after reaching the step and (ii) get reflected at the potential step. (e) (10 pts) Now suppose the electron has a kinetic energy of 5 eV. Estimate the distance the electron can penetrate the barrier.
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The boundary conditions at x = 0 are that the electron is in the left half-space and has zero kinetic energy. Show more…
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