We can see the analogy with going to the momentum representation in quantum mechanics.
2.
We can see the analogy with going to the momentum representation in quantum mechanics ( see Position and momentum space ).
3.
All equations are in the position representation; for the momentum representation the equations have to be Fourier transformed see position and momentum space.
4.
:this page has a derivation of the reverse relation where x = i hbar d / dp in the momentum representation ( start at equation 198 ).
5.
The HUP is a consequence of the fact that the momentum representation for a wavefunction is the fourier transform of its position representation ( or the same could be said for any pair of conjugate variables ).
6.
In mathematical terms, the covering group of the symplectic group is the metaplectic group, and De Gosson summarizes the mathematical reasons for the impossibility of constructing simultaneous position and momentum representations as follows : " " Hiley's'shadow phase space'approach is a reflection of the fact that we cannot construct a global chart for the metaplectic group, when it is viewed as a Lie group, that is, as a manifold equipped with a continuous algebraic structure ".
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