This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: PHYS851 Quantum Mechanics I, Fall 2008 HOMEWORK ASSIGNMENT 2: Postulates of Quantum Mechanics 1. [10 pts] Assume that A  n ) = a n  n ) but that ( n  n ) negationslash = 1. Prove that  a n ) = c  n ) is also an eigenstate of A . What is its eigenvalue? What should c be so that ( a n  a n ) =1? Solution: A  a n ) = Ac  n ) = cA  n ) = ca n  n ) = a n ( c  n ) ) = a n  a n ) . ( a n  a n ) =  c  2 ( n  n ) . Setting equal to unity requires c = radicalbig ( n  n ) . 2. [10 pts] Assume that  n ) and  a n ) are degenerate eigenstates of A with eigenvalue a n . They sat isfy ( n  n ) = ( a n  a n ) = 1 and ( n  a n ) negationslash = 1. Show that the states  a n , 1 ) =  a n ) and  a n , 2 ) =  n ) a n )( a n  n )  n ) a n )( a n  n ) are both eigenstates of A with eigenvalue a n , and are mutually orthogonal. Now assume that the system is in state  ) when A is measured. Write an expression for the proba bility 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....
View
Full
Document
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

Click to edit the document details