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Unformatted text preview: numerical solution procedures: your set of basis functions can be cleaned up and simplied without aFecting the solution you get. Answer: Using the original basis states, the solution, say the ground state of lowest energy, can be written in the form c 1 1 + c 2 2 for some values of the constants c 1 and c 2 . Now the expression for the orthogonalized functions, 1 = ( 1 2 ) 2 = ( 2 1 ) , can for given 1 and 2 be thought of as two equations for 1 and 2 that can be solved. In particular, adding times the second equation to the rst gives 1 = 1 + 2 (1 2 ) . Similarly, adding times the rst equation to the second gives 2 = 2 + 1 (1 2 ) ....
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- Fall '11