Exploring the ψ(r,t) Wave Function: Probability & Position

[S1CkFiSh]

What is the relationship between the wave function ψ(r,t) of a particle and the probability of finding the particle at position r at time t?

 

[ideasrule]

The probability of finding the particle at EXACTLY r and at EXACTLY time t is zero, just like how the probability of choosing the number 2 when given an infinite number of numbers to choose from is 0. However, the square of the wavefunction is the probability density. Given the probability density function, you find the probability of finding the particle between t1 and t2 and between r1 and r2 by integration.