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How to Prove Momentum Operator is Hermite Operator?

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Karmerlo
#1
Jun15-11, 11:42 PM
P: 14
Hi, I have little trouble in proving a proving problem ---


How to Prove Momentum Operator is Hermite Operator?


Thanks.
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haushofer
#2
Jun16-11, 01:20 AM
Sci Advisor
P: 899
Apply the definition of a Hermitian operator on the inner product (which is an integral), do a partial integration and use that wave functions have to be in L2 (and thus have certain boundary conditions at infinity).
dextercioby
#3
Jun16-11, 05:18 AM
Sci Advisor
HW Helper
P: 11,915
Whether the momentum operator for a particle in 1D is self-adjoint or not is a matter of boundary conditions. See the discussion from pages 1-3 from http://www.hep.caltech.edu/~fcp/math.../linDiffEq.pdf


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