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Kinetic Energy operator is hermitian

  • Thread starter nabeel17
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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
 

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  • #2
UltrafastPED
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See this set of notes on Hermitian operators: http://faraday.uwyo.edu/~yurid/QM/Lecture%208.pdf [Broken]
 
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