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U(1):?:SU(3) 1D:2D:3D harmonic oscillator.

  1. Apr 20, 2009 #1
    The one dimensional harmonic oscillator is associated with the group U(1) and the three dimensional harmonic oscillator is associated with the group SU(3). Is their a group associated with the two dimensional harmonic oscillator?

    Thank you for any thoughts.
  2. jcsd
  3. Apr 21, 2009 #2
    I was given the hint by Igor, thoovler@excite.com:

    "What simply connected special unitary group is bigger
    than U(1), but smaller than SU(3)?"

    My guess was SU(2), a Google search seems to confirm this.
  4. Apr 21, 2009 #3

    Ben Niehoff

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    Gold Member

    Yes, I think you are correct. If you have a copy of Goldstein (Classical Mechanics), they discuss this, as well as the SO(4) symmetry of the 1/r potential.
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