# Position representation

A way to write the wavefunction such that the position operator is: $$x (1)$$ i.e., a function that takes the wavefunction as input, and outputs another function: $$xψ(x) (2)$$
If you believe that mathematicians took care of continuous spectrum for us and that everything just works, the most concrete and direct thing that this representation tells us is that:
the probability of finding a particle between and at time
equals: $$∫x0​x1​​xψx,tdx (3)$$