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Commutating operators -Quantum

  1. Nov 9, 2013 #1
    Hello
    1. The problem statement, all variables and given/known data

    For a free particle moving in one dimension, divide the following set of operators into subsets of commuting operators:
    [P,x, H, p]

    2. Relevant equations



    3. The attempt at a solution
    I don't get the statement itself
    What does the set represents for the particle ?
    Dividing into subsets is like finding the operators that commute in the set ?

    Thanks
     
  2. jcsd
  3. Nov 9, 2013 #2
    You're just supposed to find the subsets of that set such that the commutator of every operator in a subset commutes with every other operator in that subset.


    So if we had[itex]A, B,[/itex] and [itex]C[/itex], and [itex][A,B] = 0[/itex], but [itex][A,C] \neq 0[/itex] and [itex][B,C] \neq 0[/itex], then your sets would be

    [itex]\left\{ A, B \right\}, \left\{ C\right\}[/itex]
     
  4. Nov 10, 2013 #3
    Thank you !
     
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