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Superposition state

  1. Sep 5, 2012 #1
    Structure and dynamics in the microcosm are inherently connected by the laws of quantum mechanics.
    Take, for example, a particle put in a superposition of its
    ground state
    0
    x of energy W 0
    and the first excited
    state
    1
    x of energy W 1
    . Such a superposition state is
    referred to as a wave packet. Change in the position of
    its center of mass is the closest quantum mechanical ana-log of classical motion. Solution of the Schrödinger
    equation for the particle’s wave function x yields an
    oscillatory motion with the oscillation period T
    osc
    =2 / W , where W = W 1
    − W 0
    . The larger the energy
    separation W between the two eigenstates, the faster is
    the particle’s motion in the superposition state.
    would you please explain why?
     

    Attached Files:

  2. jcsd
  3. Sep 5, 2012 #2

    Jano L.

    User Avatar
    Gold Member

    The oscillation of the wave function is faster, but whether the individual particle moves faster is not so clear. Why do you think so?
     
  4. Sep 5, 2012 #3
    If you want to google "quantum beats" you'll find all sorts of careful examples with useful pictures to help understand it. To understand what's going on with "speed" or the particle, use the fourier transform to look at the momentum-space wave function rather than the position space one.
     
  5. Dec 5, 2012 #4
    thank you for your answer!

    if wavefunctionψ=Ʃcψ(r)exp(-i/hEt)
    h should be h bar,but I cant't enter it!
    what the form of momentum-space wave function?
    best wishes!!
     
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