Final_Review

# Final_Review - University of Colorado Department of Physics...

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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 0 , 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 0 Ψ( x, t = 0) = A [exp( ik 0 x ) + exp( - ik 0 x )] Find the potential V ( x ) for which Ψ( x, t = 0) solves the time-dependent 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. 4. A normalized wave function of a particle is written as: Ψ( x, t = 0) = 1 3 χ 1 ( x ) + 1 6 χ 2 ( x ) + 1 2 χ 3 ( x ) where χ 1 , χ 2 and χ 3

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