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Uncertainty of energy in a quantum harmonic oscillator

  1. Apr 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the uncertainty of the kinetic energy of a quantum harmonic oscillator in the ground state, using

    [itex]\left\langle p^2_x \right\rangle = \displaystyle\frac{\hbar^2}{2a^2}[/itex] and
    [itex]\left\langle p^4_x \right\rangle = \displaystyle\frac{3\hbar^2}{4a^2}[/itex]

    2. Relevant equations
    [itex]\Delta E_{kin}=\sqrt{\left\langle E^2_{kin} \right\rangle - \left\langle E_{kin} \right\rangle^2} [/itex]

    [itex]\left\langle E_{kin} \right\rangle = \displaystyle\frac{\left\langle p^2_x \right\rangle}{2m} [/itex]

    3. The attempt at a solution
    With [itex]\left\langle E_{kin} \right\rangle^2[/itex] I have no problem with but am I valid in saying

    [itex]\left\langle E^2_{kin} \right\rangle = \displaystyle\frac{\left\langle p^4_x \right\rangle}{4m^2}[/itex]?
  2. jcsd
  3. Apr 4, 2013 #2


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