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Unformatted text preview: Chem 5314 homework #2 due Sept. 20, 2011 Problem 1 separation of variables The heat equation is: u t = 2 u (1) where is the thermal diffusivity of a substance, and u ( x,y,z,t ) decribes the temperature of a substance as a function of space and time. Show that the separation of variables procedure can be successfully applied to this partial differential equation to separate the space and time variables. You should obtain, as your final answer, a series of ordinary differential equations. Problem 2 particle in a box Consider a particle in a one-dimensional box of length L in its lowest energy (ground) stationary state. Calculate the probability that the particle is a) in the left half of the box b) in the middle third of the box. c) Draw a picture of the wavefunction and associated probability for each of parts a) and b) and justify that your answers make sense in terms of these pictures....
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