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Evaluating commutator with hamiltonian operator

  1. Jan 15, 2010 #1
    Evaluate the commutator [H,x], where H is Hamiltonian operator (including terms for kinetic and potential energy). How does it relate to p_x, momentum operator (-ih_bar d/dx)?
  2. jcsd
  3. Jan 16, 2010 #2

    The Hamiltoinan in a one dimensional space is defined as [tex]H=-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x)[/tex]. So the commutator [H,x] is

    [tex][H,x]=Hx-xH=[-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x)]x-x[-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x)][/tex]. Continue this calculation and then by catching a glimpse of the definition of the operator [tex]p[/tex], you can get what the relation is.

    Last edited: Jan 16, 2010
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