# pmwiki - January-14-12 7:43 PM Physics 3380 Quantum II...

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Physics 3380, Quantum II Assignment 1 Due: January 27 in class January-14-12 7:43 PM Title Page 1

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The Gram-Schmidt procedure allows one to find an orthonormal basis from one that is not orthonormal but satisfies all other properties of a basis (actually they just need to be linearly independent vectors). This procedure is usually taught in a basic linear algebra course and should be available in any book on the subject. The procedure goes as follows: Suppose you have a 3 dimensional space with a basis given by: Clearly, these vector are linearly independent and form a basis (this is required for the procedure to work!) The we can find an orthonormal basis as follows: Normalize the first vector and take this as the first orthonormal basis vector: i. Find the projection of the second vector along the first orthonormal vector and subtract it from itself. Then normalize the result to get the second orhtonormal basis vector: ii. First some background information: Problem 1 January-13-12 10:40 AM Problem 1 Page 1
Take the third vector and subtract its projections along the first two orthonormal vectors from itself and then normalize the resulting

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## This note was uploaded on 02/16/2012 for the course PHYSICS 3380 taught by Professor M.gericke during the Winter '12 term at Manitoba.

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pmwiki - January-14-12 7:43 PM Physics 3380 Quantum II...

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