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A 3D oscillator trapped away from centre

  1. Oct 7, 2016 #1
    The spherical oscillator problem is for a potential centered at the origin.. but what if the particle is confined to oscillate at a small shift by a small (not infinite) barrier? The potential is now centered about the new position.. Could someone please suggest a way to solve the problem for the energy levels?
     
  2. jcsd
  3. Oct 7, 2016 #2

    Vanadium 50

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    Can you write down the potential?
     
  4. Oct 7, 2016 #3
    I assume the general form of the potential is
    1/2 m w^2 (r-r0)^2
     
  5. Oct 7, 2016 #4

    Vanadium 50

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    Then it can be solved using a change of variables,
     
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