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Kinetic Energy operator is hermitian

  1. Sep 25, 2013 #1
    The problem asks to show that the kinetic energy operator is Hermitian.



    The operator is given as T= -h^2/2mΔ but I know I can also write it as p^2/2m which would be

    (- ih∇)(-ih∇). My main question is if I can prove this in 1-D so that T=(-h^2/2m)d^2/dx^2
    does that generalize to 3-d? Is it proven in 3 dimensions then? If not I'm not sure where to even begin in 3D
     
  2. jcsd
  3. Sep 26, 2013 #2

    UltrafastPED

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    See this set of notes on Hermitian operators: http://faraday.uwyo.edu/~yurid/QM/Lecture%208.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
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