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Observable and Operators - Obtain an expression

  1. Mar 31, 2012 #1

    vmr101

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    Gold Member

    1. The problem statement, all variables and given/known data
    a) Two observables A and B are represented by operators A(hat) and B(hat), which obey the following commutation relation: [A(hat), B(hat)] = iC,

    where C is the real number. Obtain an expression for the product of the uncertainties ΔAΔB.

    b) Hadrons, such as protons, neutrons and mesons are composed of point-like elementary particles known as quarks. The strong interaction between two quark is described in the confinement region by a potential of the form:

    V(r) = br,

    where r is the seperation between two quarks and b is a constant. It is possible to form bound states of a quark and an antiquark in a system known as quarkonium. Use an argument based on the uncertainty principle to obtain an expression for the ground state energy of quarkonium.
    Hint Assume the reduced mass of quarkonium is m(^lower subscript)Q

    2. Relevant equations
    [A(hat), B(hat)] = iC,
    and
    V(r) = br,


    3. The attempt at a solution
    I am not even sure where to start with this! Any help and guidance is appreciated.
     
    Last edited: Mar 31, 2012
  2. jcsd
  3. Apr 12, 2012 #2

    vmr101

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    Gold Member

    The attachment is what i have came up with for 6a), can anyone give me some feedback?
    Cheers.
     

    Attached Files:

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