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Expectation value of momentum in symmetric 2D H.O

  1. Jun 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider the following inital states of the symmetric 2D harmonic oscillator

    ket (phi 1) = 1/sqrt(2) (ket(0)_x ket(1)_y + ket (1)_x ket (0)_y)

    ket (phi 2) = 1/sqrt(2) (ket(0)_x ket(0)_y + ket (1)_x ket (0)_y)

    Calculate the <p_x (t)> for each state

    2. Relevant equations


    3. The attempt at a solution

    I am not sure how to work with these kets, I know that for the expectation value using you would do
    <phi_1 | p_x (t) | phi_2>

    but I don't know how to represent p_x (t) in the notation used in the kets


    Any help would be much appreciated.
     
    Last edited: Jun 10, 2015
  2. jcsd
  3. Jun 10, 2015 #2

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    The expectation value for an operator on a state is <state 1| operator |state 1>. You wrote <state 1| operator |state 2>. Note the 2 in the last ket. That's a transition amplitude as induced by the operator.

    Look in your text for a representation of the momentum operator. You should find it near he Heisenberg uncertainty formula, or the Schrodinger equation or some such. You probably want a derivative with some constants.

    Notice that the problem says "initial states." So these are not the wave functions. These are the t=0 values. It does not give the x dependence, nor the t dependence. You will need to do some reading in your text to find the 2-D harmonic oscillator and the general solution for it.
     
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