How to Prove Momentum Operator is Hermite Operator?

[Karmerlo]

Hi, I have little trouble in proving a proving problem ---


How to Prove Momentum Operator is Hermite Operator?


Thanks.

 

[haushofer]

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]

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/differentialEquations/linDiffEq.pdf