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Deriving hermite differential equation from schrødinger harm oscillator

  1. Jan 21, 2016 #1

    georg gill

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    Gold Member

    1. The problem statement, all variables and given/known data

    I am trying to obtain the hermite polynomial from the schrødinger equation for a har monic oscillator. My attempt is shown below. Thank you! The derivation is based on this site:

    http://www.physicspages.com/2011/02/08/harmonic-oscillator-series-solution/



    3. The attempt at a solution
    upload_2016-1-21_15-7-36.png
    upload_2016-1-21_15-8-11.png
    upload_2016-1-21_15-9-26.png
    upload_2016-1-21_15-9-59.png
    however the book says:
    upload_2016-1-21_15-12-38.png
    upload_2016-1-21_15-13-2.png
     
  2. jcsd
  3. Jan 21, 2016 #2

    blue_leaf77

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    Seems like your mistake lies in your calculation of ##\frac{\partial^2 \psi}{\partial y^2}##. I suggest that you check again on this point to see whether you had left out one term.
     
  4. Jan 21, 2016 #3

    georg gill

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    Gold Member

    thanks!
     
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