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Unformatted text preview: of being anywhere inside this box, and zero probability of being outside the box. (a)Calculate the probability distribution of the position of the particle, making sure that the integrated probability is 1. (b) Calculate the standard deviation x of its position, defined as x = [<x 2 > -<x> 2 ] 1/2 where <f(x)> means take the average value of f(x) integrated over the probability distribution. (c)Using Heisenbergs uncertainty principle, estimate the standard deviation v of its velocity distribution in terms of L and m. (15 points) 2. The phase velocity of a surface wave on a liquid depends on its wavelength via the relation v p = 2 S / "# where S is the surface tension, is the wavelength and is the liquid density. Calculate the group velocity of the surface waves in terms of these quantities. (10 pts)...
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