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I understand how to transform between position space and momentum space; it's a Fourier transform:

[tex]\varphi|p>=\frac{1}sqrt{2\hbar\pi}\int_{\infty}^{\infty} <x|\varphi> exp(-ipx/\hbar)dx[/tex]

But I can't figure out how to transform the operators. I know what they transform into (e.g., the p operator in position space goes to 'p' in momentum space), but not how.

Any help? Thanks