General question about wavefunctions

[phi1123]

Homework Statement

Is it possible given a wavefunction ψ(x,t) to find the probability that the particle is at a particular location over an interval of time?

Homework Equations

The Attempt at a Solution

Intuitively, given that the probability of finding the particle in a region a<x<b at a time t is ∫_a^b|ψ(x,t)|²dx, i would guess that the probability of finding the particle t_i<t<t_f at the point x would be ∫_ti^tf|ψ(x,t)|²dx. However, this leads to a bit of a paradox: this integral can leads to probabilities greater than 1, which would suggest that I am missing something pretty critical.

 

[sweet springs]

Hi.
If you observe the position at t=ti wave function changes or contracts so it is a mess.
If you do not observe, you cannot say anything about position at t = ti or about staying in point x.
Regards.