# Kinetic Energy operator is hermitian

1. Sep 25, 2013

### nabeel17

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. Sep 26, 2013

### UltrafastPED

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