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Unformatted text preview: Quantum Mechanics I, Review Problems for Midterm 2 1 I: Scattering A. HalfInfinite Square Well Consider the potential shown at the right where the potential is infinite for x < 0, zero in the region, ≤ x < L and V in the region x ≥ L . 1. Are there any bound energy eigenstates for this well? How can you tell and how many are there? 2. On the graph to the right, assume that there is at least one bound state and sketch that state, including all the relevant properties. x L E b ? x Ψ H x L ¥ V H x L V Now, consider the case where E > V : 3. Are there any states for this energy range? How many? 4. For any allowable energy in this range, what is the general solution of the time independent Schr¨ odinger equation? 5. Imagine that the solution to part 4 represents a particle coming in from the right and scattering off the well. What is the ratio of the amplitudes of the incoming and outgoing waves? Is this surprising? PHYS 3220 Midterm Review 2009 c S. Goldhaber, and the Physics Education Group University of Colorado, Boulder Quantum Mechanics I, Review Problems for Midterm 2 2 II: Measurement and Quantum Mechanics Formalism A. Measurement Consider a particle of mass m in a 1D infinite square well with V ( x ) = 0 for 0 < x < a , and V = ∞ elsewhere....
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.
 Fall '08
 STEVEPOLLOCK
 mechanics

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