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Unformatted text preview: University of Colorado, Department of Physics PHYS3220, Fall 09, Some final review problems 1. At time t=0, a particle is represented by the wave function: Ψ( x,t = 0) = A x a , if 0 ≤ x ≤ a A b x b a , if a ≤ x ≤ b , else where a and b are constants. At which x does the probability density peak? Calculate the probability to find the particle to the left of a (i.e. for x ≤ a ). 2. Consider the following wave function for a particle of mass m at time t = 0, characterized by a positive constant k Ψ( x,t = 0) = A [exp( ik x ) + exp( ik x )] Find the potential V ( x ) for which Ψ( x,t = 0) solves the timedependent Schr¨ odinger equation? Does Ψ( x,t = 0) represent an acceptable physical state? Justify your answer. 3. How does the probability current density J ( x,t ) change with time, if the system is in a stationary state (energy eigenstate)? Explain your answer....
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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
 Physics

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