= Position and momentum space
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One of the main reasons why physicists are obsessed by this topic is that position and momentum are mapped to the <phase space coordinates> of <Hamiltonian mechanics>, which appear in the <matrix mechanics> formulation of <quantum mechanics>, which offers insight into the theory, particularly when generalizing to <relativistic quantum mechanics>.
One way to think is: what is the definition of space space? It is a way to write the wave function $\psi_x(x)$ such that:
* the position operator is the multiplication by $x$
* the momentum operator is the derivative by $x$
And then, what is the definition of momentum space? It is of course a way to write the wave function $\psi_p(p)$ such that:
* the momentum operator is the multiplication by $p$
https://physics.stackexchange.com/questions/39442/intuitive-explanation-of-why-momentum-is-the-fourier-transform-variable-of-posit/39508\#39508 gives the best idea intuitive idea: the <Fourier transform> writes a function as a (continuous) sum of plane waves, and each plane wave has a fixed momentum.
Bibliography:
* https://en.wikipedia.org/wiki/Position_and_momentum_space