Homework4

# Homework4 - Physics 401 Homework#4 1...

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Physics 401 - Homework #4 1) Particle-in-a-box (three points each). Consider a particle of mass (m) confined in a one- dimensional box between x = 0 and x = L. At t = 0 the state of the system is given by a square function: L x 2 ) ( , 4 3 4 L x L 0 ) ( x , otherwise a) We wish to write this wavefunction as a sum of energy eigenstates: n n n x a x ) ( ) ( Calculate the correct set of expansion coefficients {a n } for this expression. b) Suppose that at t = 0 we decide to measure the energy of the system. What is the probability that the result of the measurement will be 2 2 2 2 9 mL E ? c) Suppose that we perform the energy measurement, and that the result of the measurement is, in fact, 2 2 2 2 9 mL E . What will be the new wavefunction for the system after this energy measurement? d) Now we let the new wavefunction evolve in time. What will be the fully time-dependent wavefunction, ? ) , ( t x e) After the energy measurement, will the position probability distribution for the system change as a function of time, or will it be constant in time? Explain your answer.

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Homework4 - Physics 401 Homework#4 1...

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