How to Prove Momentum Operator is Hermite Operator?by Karmerlo Tags: hermite operator, momentum operator 

#1
Jun1511, 11:42 PM

P: 14

Hi, I have little trouble in proving a proving problem 
How to Prove Momentum Operator is Hermite Operator? Thanks. 



#2
Jun1611, 01:20 AM

Sci Advisor
P: 869

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).




#3
Jun1611, 05:18 AM

Sci Advisor
HW Helper
P: 11,863

Whether the momentum operator for a particle in 1D is selfadjoint or not is a matter of boundary conditions. See the discussion from pages 13 from http://www.hep.caltech.edu/~fcp/math.../linDiffEq.pdf



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