3890ps2_10 - Chem 3890 Physical Chemistry I Fall 2010...

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Chem 3890 Physical Chemistry I Fall 2010 Chemistry 3890 Problem Set 2 Fall 2010 Due: in class, Friday, September 17 To facilitate accurate grading of your assignments, your printouts should have: In and Out statements. That is, the work you hand in must be a printout of an evaluated notebook. Problem numbers (given either in Section headings or in text boxes). Problem solutions in the order assigned. Handwritten and Mathematica parts of a solution should appear on contiguous sheets. Each problem in a separate notebook (or at least a separate Section ). Analytical answers Simplify -ed as far as possible. Scratch work labeled as such if present, but preferably not present at all. No 30-page tables or error messages! (Very large output statements should be hidden if generated: use the semicolon ; after a command to suppress output.) When plotting functions, it is usually helpful to use (or at least try) the option PlotRange -> All . Oth- erwise, the default range of the function plotted might be severely restricted, and the plot correspondingly uninformative. Problem 1 (This problem should be worked by hand: ) You have seen in class that the classical equations of motion for a single particle of mass m moving along the x -axis in the presence of a potential V ( x ) can be written in the form d x d t = p m (1a) d p d t = - ∂V ∂x . (1b) In general, the system is described by a Hamiltonian H , which is a function of the particle coordinate x and momentum p , H = H ( x,p ). For any Hamiltonian H , the fundamental classical equations of motion are given by Hamilton’s equations, which are d x d t = + parenleftbigg ∂H ∂p parenrightbigg x (2a) d p d t = - parenleftbigg
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