1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Commutator of f(x) and x

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Is the commutator of x and any function of x zero?

    2. Relevant equations
    Taylor's theorem allows such a function to be expanded into polynomials, so that [f(x),x] may be expanded into terms of [x^n,x], which are all zero. Hence, f(x) and x commute.

    3. The attempt at a solution

    Is this a valid demonstration?
  2. jcsd
  3. Sep 18, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You don't need a Taylor expansion. What do you think is x(f(x) - f(x)x?
  4. Sep 19, 2011 #3


    User Avatar
    Science Advisor
    Homework Helper

    This is true iff X and f(X) have the same domain, i.e. the domain of X is invariant.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook