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.../linDiffEq.pdf

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

haushofer Recognitions: Science Advisor	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 Blog Entries: 9 Recognitions: Homework Help Science Advisor	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