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Unformatted text preview: as a  H  A , where according to chapter 3.5.3, the Hamiltonian is H = h 2 2 m 2 x 2 Compare the ground state energy with the exact value, E 1 = h 2 2 / 2 m 2 (Hints: i x ( x ) d x = 3 / 6 and i x 2 ( x ) 2 d x = 5 / 30) Answer: To satisfy the normalization requirement that the particle must be somewhere, you need a  A = 1, or substituting for , 1 = a ax ( x )  ax ( x ) A =  a  2 a x ( x )  x ( x ) A And by denition, chapter 2.3, the nal inner product is just the integral i x 2 ( x ) 2 d x which is given to be 5 / 30. So you must have  a  2 = 30 5...
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 Fall '11
 Dr.DanielArenas
 mechanics

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