Position and momentum space | 🗖 nosplit | ↑ parent "Uncertainty principle" | 103, 3, 205

🗖 nosplit | ⇓ toc | ↑ parent "Uncertainty principle" | Wikipedia | 103, 3, 205

One way to think is: what is the definition of space space? It is a way to write the wave function

ψ_{x} (x)

such that:

the position operator is the multiplication by $x$
the momentum operator is the derivative by $x$

And the, what is the definition of momentum space? It is of course a way to write the wave function

ψ_{p} (p)

such that:

the momentum operator is the multiplication by $p$

Bibliography:

https://physics.stackexchange.com/questions/39442/intuitive-explanation-of-why-momentum-is-the-fourier-transform-variable-of-posit/39508#39508 gives the best idea: the Fourier transform writes a function as a (continuous) sum of plane waves, and each plane wave has a fixed momentum.
https://en.wikipedia.org/wiki/Position_and_momentum_space

Table of contents | 103, 3, 205
- 1. Position representation | 18 | 🔗 link | 🗖 nosplit | ↑ parent "Position and momentum space"
- 2. Position operator | 36 | 🔗 link | 🗖 nosplit | ↑ parent "Position and momentum space"
- 3. Momentum operator | 48 | 🔗 link | 🗖 nosplit | ↑ parent "Position and momentum space"

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