HW #4 - . Check that the matrix you constructed satises 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 de±nite 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 satises 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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