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Unformatted text preview: Problem Set 11 Note: The is the last problem set and is due December 03 by 9:00 pm. Please return directly to me in my office Rutherford 321. If Im not there slip your assignment below my door. 1. I have a system of N particles of masses m each. These particles are only constrained to move on a one dimensional surface along say x-direction. I suspend the system between two infinite walls placed at x = 0 and x = a respectively. The system therefore behaves as a one dimensional box of length a (see figure below): x = 0 x = a Imagine now that at time t = 0 the state of each particle is given by the following wave- function: ( x, 0) = Ax 2 ( x 2- a 2 )( x + 3 a ) where A is the normalisation constant. Determine this constant and answer the following questions: (a) How many particles are found at the left half of the wire, i.e at 0 &lt; x a 2 at t = 0? (b) How many particles have energies greater than thirty-six times the ground state energy at t = 0?...
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