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Homework Help: Hamiltonian solving

  1. Dec 10, 2009 #1
    how would you solve the hamilton - jacobi equation for something with a hamiltonian with mixed terms like 1/2(p1q2 + 2p1p2 + (q1)^2)

    well its quite trivial obtaining the HJ equation since there is no time dependence,

    1/2( (ds/dq1)q2 + 2(ds/dq1)(ds/dq2) + (q1)^2 ) = E

    I cant see how youw would separate the variables otherwise we could simple set
    H(q1,p1) = E1 amd H(q2,p2) = E2 .

    However I am stumped on how to do it for the above equation with mixed terms.
     
  2. jcsd
  3. Dec 10, 2009 #2
    I guess I did not phrase the question well.

    The issue is I have a given hamiltonian H = 1/2(p1q2 + 2p1p2 + (q1)^2)

    I need to solve this and I chose to begin by using the hamilton - jacobi equation and since we have no time dependence . If S is the hamilton action function then

    ((ds/dq1)*q1 + 2(ds/dq1)(ds/dq2) + (q1)^2) = E where E is now energy.

    How would you go about solving this differential equation?
     
  4. Dec 11, 2009 #3
    Actually this is quite trivial..thank you anyway.
     
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