# HW #4 - Check that the matrix you constructed satis±es all...

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Physics 591 - Homework Set # 4 Due: Monday, September 20 5 pm 1. Consider example 4.2.1 discussed in class. In the basis in which is diagonal the operator is given by there are 1000 particles in a state a) Find the expectation value for b) Now assume that we measure . List all of the following: the possible outcomes; the probability for each of those outcomes; the number of particles that will have a definite value of equal to each of the possible outcomes (assume 1000 is large enough). c) Compute the density matrix of the mixed ensemble that results after the measurement of
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Unformatted text preview: . Check that the matrix you constructed satis±es all the properties of density matrices. d) Compute the average e) Repeat parts (a) and (d) for the operator 2. a) (4.2.2) Show that for a real wave function , the expectation value of momentum vanishes, that is: . (Hint: show that the probabilities for the momenta are equal.) Generalize this result to the case where is real and c an arbitrary (real or complex) constant. b) (4.2.3) Show that if has mean momentum , then has mean momentum ....
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