851HW1_09 - HOMEWORK ASSIGNMENT 1: Due Monday, 9/14/09...

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Unformatted text preview: HOMEWORK ASSIGNMENT 1: Due Monday, 9/14/09 PHYS851 Quantum Mechanics I, Fall 2009 1. What is the relationship between ( | ) and ( | ) ? What is the relationship between the matrix elements of M and the matrix elements of M ? Assuming that H = H , what is ( n | H | m ) in terms of ( m | H | n ) ? 2. Use the matrix representation and summation notation to prove that ( AB ) = B A , where A and B are both operators. Use summation notation to expand ( | AB | ) in terms of the constituent matrix elements and vector components? 3. Consider the discrete orthonormal basis {| m )} , m = 1 , 2 , 3 ,... ,M that spans an M-dimensional Hilbert space, H M . (a) Show that the identity operator, I = m | m )( m | , satisfies I 2 = I . (b) Form a new projector, P , by removing the state | 3 ) , i.e. P = m negationslash =3 | m )( m | . Does P 2 = P ? Is P also the identity operator?...
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This note was uploaded on 12/04/2011 for the course PHY 7070 taught by Professor Smith during the Spring '11 term at Wisconsin.

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851HW1_09 - HOMEWORK ASSIGNMENT 1: Due Monday, 9/14/09...

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