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Unformatted text preview: Chemistry 550 / 475 – Homework Assignments #78 due: Friday, November 18th at 5:00 pm Readings : Chapters 6 and 8 in Levine Problem 1  Noninteracting particles. Consider the case of N noninteracting quantum mechanical particles labeled by the coordinates x 1 , . . ., x N . Each is subjected to an external potential energy of the form V ( x k ), 1 ≤ k ≤ N. a. Write down the total Hamiltonian and corresponding timeindependent Schr¨ odinger equa tion describing this system. What is the physical meaning of the eigenvalue appearing in the latter? Be sure to explicitly note the coordinates of the total Nparticle wave function Ψ appearing within. b. Make a separation of variables in Ψ expressing it as the product of singleparticle wave functions. Does interchanging the ordering of any pair of coordinates have any affect on Ψ? c. Use the previous wavefunction ansatz to decompose the total Schr¨ odinger equation into a collection of N single particle Schr¨ odinger equations. What are the eigenvalues of each equation and how do they relate to the eigenvalue from part ( a...
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This note was uploaded on 01/18/2012 for the course CHEM 550/475 taught by Professor Davidj.masiello during the Fall '11 term at University of Washington.
 Fall '11
 DavidJ.Masiello
 Chemistry

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