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

  • Thread starter Spinnor
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  • #1
Spinnor
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
Spinnor
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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.
 
  • #3
Ben Niehoff
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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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