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What is the name of this Hamiltonian?

  1. Jul 29, 2014 #1
    Hello (and sorry for this stupid question),

    Could someone tell me the name of this Hamiltonian

    [tex] H = \left(\dfrac{p^2+q^2}{2}\right)^2 [/tex]

    Thanks in advance
     
  2. jcsd
  3. Jul 29, 2014 #2

    jedishrfu

    Staff: Mentor

  4. Jul 29, 2014 #3
    I'm just looking for the name that is called in the scientific literature. I am not looking for the Hamiltonian theory.
     
  5. Jul 29, 2014 #4

    jedishrfu

    Staff: Mentor

    In the article, it shows a specific hamiltonian similar to yours and relates it to a "Heisenberg group" under the topic Sub-Riemannian manifolds.

    Its unfortunate that the URL didn't directly jump there as expected.
     
  6. Jul 29, 2014 #5

    jedishrfu

    Staff: Mentor

    Or maybe this one:

    http://www.unige.ch/~hairer/poly_geoint/week1.pdf
     
  7. Jul 29, 2014 #6
    Ok, Thank you jedishrfu.

    However, there are subtle differences between these two Hamiltonians. "My" can be thought of as the Hamiltonian of the harmonic oscillator squared:

    [tex] H = H_{HO}^2 [/tex]

    where

    [tex] H_{HO} = \dfrac{1}{2}(p^2+q^2) [/tex].
     
    Last edited: Jul 29, 2014
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