Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Operator Language?

  1. Mar 13, 2010 #1
    When linear operators A and B act on a function ψ(x), they don't always commute. A clear example is when operator B multiplies by x, while operator A takes the derivative with respect to x. Then

    which in operator language means that


    To get the last equation they divided through by ψ but why is it true? I guess what I'm trying to say is that the second equation makes no sense => d/dx*x - x*d/dx doesn't always equal 1... so why do they say that?
  2. jcsd
  3. Mar 13, 2010 #2
    First, they don't divide it by [itex]\Psi[/itex]; they simply consider it the argument of the operator AB-BA. It's akin to denote a function by f only, instead of f(x), where the variable is explicit.

    Second, in this context, d/dx*x - x*d/dx doesn't always equal 1; in fact, it never equals 1: it equals the identity operator I, the one that satisfies [itex]I\Psi=\Psi[/itex].
  4. Mar 13, 2010 #3
    Thanks for stating it so clearly and concisely. Many issues were resolved.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook