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Quantizing a hamiltonian

  1. Jan 8, 2009 #1
    1. The problem statement, all variables and given/known data
    The Lagrangian of a non-relativistic particle propagating on a unit circle is
    [tex]
    L=\frac{1}{2}\dot{\phi}^{2}
    [/tex]

    where ϕ is an angle 0 ≤ ϕ < 2π.
    (i) Give the Hamiltonian of the theory, and the Poisson brackets of the ca-
    nonical variables. Quantize the theory by promoting the Poisson brackets into
    commutators, and write the angular momentum operator, L, which is the con-
    jugate (momentum) variable of ϕ, in the position representation. Note that in
    the position representation
    [tex]
    \hat{\phi}|\phi\rangle=\phi|\phi\rangle\;,\;\langle\phi'|\phi\rangle=\delta(\phi'-\phi)
    [/tex]
    2. Relevant equations



    3. The attempt
    i am stuck on the part where i have to write down L, how do i find its form in the $\phi$ representation? Please help
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 9, 2009 #2
    Anyone?
     
  4. Jan 11, 2009 #3
    Please some1 help!
     
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