Hw78 - Chemistry 550 475 – Homework Assignments#7-8 due Friday November 18th at 5:00 pm Readings Chapters 6 and 8 in Levine Problem 1

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Unformatted text preview: Chemistry 550 / 475 – Homework Assignments #7-8 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 time-independent 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 N-particle wave function Ψ appearing within. b. Make a separation of variables in Ψ expressing it as the product of single-particle wave functions. Does interchanging the ordering of any pair of coordinates have any affect on Ψ? c. Use the previous wave-function 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.

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Hw78 - Chemistry 550 475 – Homework Assignments#7-8 due Friday November 18th at 5:00 pm Readings Chapters 6 and 8 in Levine Problem 1

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