How is the Wavefunction ψ(x) Related to the Probability Distribution P(x)?

[zak8000]

Homework Statement

wave function of a particle in one dimension

wave function of a particle in one dimension at time t=0 given by
psi(x,0) = A(x^0.5)*(e^-ax) for x>0 or x=0
psi(x,0) = 0 for x<0

where x is in nms and a = 1nm

where is the particle most likely to be found? or for what value of x is P(x) a maximum

Homework Equations

The Attempt at a Solution

i first normalised it to find A=2a

 

[kuruman]

How is the wavefunction ψ(x) related to the probability distribution function P(x)?