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# HW8 - University of Colorado Department of Physics PHYS3220...

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University of Colorado, Department of Physics PHYS3220, Fall 09, HW#8 due Wed, Oct 15, 2PM at start of class 1. Minimum energy (Griffiths, Problem 2.2, Total: 10 pts) Show that E must exceed the minimum value of V ( x ), for every normalizable solution to the time-independent Schr¨ odinger equation. 2. An infinitely high potential step (Total: 10pts) Examine the limiting case of an infinitely high potential step, i.e. V 0 → ∞ (the energy E kept constant). a) Find the wave function in the limiting case. b) Are the wave function and its first derivative continuous at the boundary x = 0? Explain your result. 3. Some quantitative problems (Total: 10pts) a) An electron with a kinetic energy of 10 eV at large negative values of x is moving from left to right along the x -axis. The potential energy is given by: V ( x ) = ( 0 x < 0 20eV , x 0 Estimate the order of magnitude of the distance the electron can penetrate the barrier. b) Repeat part a) for a 70 kg person initially moving at 4 ms - 1 and running into a

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