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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 ( ψ  φ ) and ( φ  ψ ) ? What is the relationship between the matrix elements of ˆ M † and the matrix elements of ˆ 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 ( φ  AB  ψ ) † 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 Mdimensional Hilbert space, H M . (a) Show that the identity operator, ˆ I = ∑ m  m )( m  , satisfies ˆ I 2 = ˆ I . (b) Form a new projector, ˆ P , by removing the state  3 ) , i.e. ˆ P = ∑ m negationslash =3  m )( m  . Does ˆ P 2 = ˆ P ? Is P also the identity operator?...
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This note was uploaded on 12/02/2010 for the course PHYSICS 851 taught by Professor M.moore during the Fall '09 term at Michigan State University.
 Fall '09
 M.Moore
 mechanics, Work

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