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What is the velocity operator?

  1. Feb 7, 2010 #1
    1. The problem statement, all variables and given/known data
    I was wondering how to construct the velocity operator


    2. Relevant equations
    P=MV


    3. The attempt at a solution
    Since P=MV, i used the linear momentum operator and divided by M to get V. Is this the right way to construct an operator from linear momentum and position operators? I did something similar to this to construct the hamiltonian and got the hamiltonian operator. I was wondering about this because i wanted to see if linear momentum and velocity commute. I calculated that they do commute, can someone verify this?
     
  2. jcsd
  3. Feb 7, 2010 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    Yes, yes and yes. Dividing the momentum operator by m gives you the velocity operator. If an operator is a constant times another operator, the two operators commute. You may wish to prove this last result to convince yourself if you are not sure.
     
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