Unformatted text preview: numerical solution procedures: your set of basis functions can be cleaned up and simpli±ed 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 ψ 1 + c 2 ψ 2 for some values of the constants c 1 and c 2 . Now the expression for the orthogonalized functions, ¯ ψ 1 = α ( ψ 1 − εψ 2 ) ¯ ψ 2 = α ( ψ 2 − εψ 1 ) , can for given ¯ ψ 1 and ¯ ψ 2 be thought of as two equations for ψ 1 and ψ 2 that can be solved. In particular, adding ε times the second equation to the ±rst gives ψ 1 = ¯ ψ 1 + ε ¯ ψ 2 α (1 − ε 2 ) . Similarly, adding ε times the ±rst equation to the second gives ψ 2 = ¯ ψ 2 + ε ¯ ψ 1 α (1 − ε 2 ) ....
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 Fall '11
 Dr.DanielArenas
 mechanics

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