newassign10 - Problem Set 10 Note The following problem set...

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Problem Set 10 Note: The following problem set is due November 21 by 9:00 pm. Please return directly to me in my office Rutherford 321. If I’m not there slip your assignment below my door. 1. I put a quantum particle of mass m in a box of length L . The position of the particle is random and is given by wavefunctions depending on what energies the particle has. Imagine I detect the particle at a point x = x 0 inside the box such that 0 < x 0 < L at a time t = 0. Answer the following questions quantitatively: (a) Determine the probability of finding the particle at the same point x 0 at a later time t 1 > 0. What is the probability of finding the particle at a different point x = x 1 at the same time t 1 ? Analyse this using the time dependent wavefunction of the system. (b) Now consider the following scenario: the instant I detect the particle at x = x 0 both the walls of the box suddenly fall down so that the particle has a free access to go anywhere. What is the probability of finding the particle at the same point but at a later time t 1 ?
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