assignment7 - PHYS122 2010W Assignment 7 Due 17:00 Thursday...

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PHYS122 2010W Assignment 7 Due: 17:00 Thursday 2010-03-11
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PHYS122 Assignment 7 UW User ID: - Your UW User ID is not the same as your Student Number. Surname: Given Name: 1. Consider a particle of mass m in an infinite square well of width a . The wave function is given by ψ ( a ) = A sin( kx ) where k = nπ/a , n = 1 , 2 , 3 ... For a particle in the ground state, n = 1 , calculate (a) (2) the expectation value of the position, h x i , where ˆ x = x is the position operator h x i = (b) (2) the expectation value of the square of the position, x 2 , where x 2 is the operator x 2 = (c) (0) the square of the uncertainty in the position, Δ x 2 = x 2 - h x i 2 . Δ x 2 = (d) (2) the expectation value of the momentum, h p i , where ˆ p = - i ~ d dx is the “momentum operator” h p i = (e) (2) the expectation value of the square of the momentum, p 2 , where - ~ 2 d 2 dx 2 is the operator p 2 = (f) (0) the square of the uncertainty in the momentum, Δ p 2 = p 2 - h p i 2 . Δ x 2 = (g) (2) Calculate the product Δ x Δ p and compare your answer to the expected result.
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