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## Main Question or Discussion Point

Dear all,

in basic QM books the position and momentum operators (continuous eigenvectors) are introduce by means of the dirac delta and some analogies are made with the infinite dimensional, but discrete case in order to provide some intuition for the integral formulas presented. My knowledge is limited, but it seems to me that thee formulas apply in the distribution sense. Can anybody explain to me how the position and momentum operators are treated in a rigorous way? An outline will do.

Thanks for any help!

Goldbeetle

in basic QM books the position and momentum operators (continuous eigenvectors) are introduce by means of the dirac delta and some analogies are made with the infinite dimensional, but discrete case in order to provide some intuition for the integral formulas presented. My knowledge is limited, but it seems to me that thee formulas apply in the distribution sense. Can anybody explain to me how the position and momentum operators are treated in a rigorous way? An outline will do.

Thanks for any help!

Goldbeetle