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Unformatted text preview: PHYS851 Quantum Mechanics I, Fall 2007 HOMEWORK ASSIGNMENT 2: Postulates of Quantum Mechanics 1. [10 pts] Assume that A  φ n ) = a n  φ n ) but that ( φ n  φ n ) negationslash = 1. Prove that  a n ) = c  φ n ) is also an eigenstate of A . What is its eigenvalue? What should c be so that ( a n  a n ) =1? 2. [10 pts] Assume that  φ n ) and  a n ) are degenerate eigenstates of A with eigenvalue a n . They sat isfy ( φ n  φ n ) = ( a n  a n ) = 1 and ( φ n  a n ) negationslash = 1. Show that the states  a n , 1 ) =  a n ) and  a n , 2 ) =  φ n )− a n )( a n  φ n )  φ n )− a n )( a n  φ n ) are both eigenstates of A with eigenvalue a n , and are mutually orthogonal. Now assume that the system is in state  ψ ) when A is measured. Write an expression for the probability to obtain the result a n . Write down the state of the system immediately after the measurement, assuming that a n was obtained by random chance....
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.
 Fall '08
 MichaelMoore
 mechanics, Work

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