Determined by the mathematics, i.e. how the momentum operator is defined in quantum mechanics. https://en.wikipedia.org/wiki/Momentum_operator https://en.wikip

Determined by the mathematics, i.e. how the momentum operator is defined in quantum mechanics. https://en.wikipedia.org/wiki/Momentum_operator https://en.wikipedia.org/wiki/Momentum_operator As GP said, position and momentum for a given system are the same thing represented using different basis vectors. Let's use an more intuitive example, outside of quantum mechanics, in regular linear algebra in R3. If you have a something in 3D space, you can come up with multiple different coordinate systems to describe things in that space. Once you specify the position of an object in one coordinate system, the position of that object in all other coordinate systems is also determined. In quantum mechanics, position and momentum have this sort of relationship. If you specify the position distribution of a something, you can transform it to its corresponding distribution in momentum space. Another comparison is with frequency/time of a signal. Once you specify how a signal looks over time, its frequency spectrum is determined and vice versa; the two are Fourier transforms of each other.