# Wavefunction with specific values

1. Nov 12, 2013

### Gringema

1. The problem statement, all variables and given/known data
Near a certain position xA, a quanton's wavefunction ψ(xA)=-0.3 in some units. Near a certain position xB, a quanton's wavefunction ψ(xB[\SUB])=0.12 in the same units. If we do an experiment to locate the quanton, how many times more likely is i that the result is in a small range near xA than in a range twice as large near xB? Please explain.

2. Relevant equations
ψ(x)=ψ/sqrt(Δx)
|ψ|2=Pr(x)

3. The attempt at a solution
I used the definitions of wavefunction and amplitude to get Pr(x)=|ψ(x)|2Δx.
So Pr(xA)=(-0.3)2=0.09
And Pr(xB)=2(0.12)2=0.0288
Therefore Pr(xA)=3.125Pr(xB)

2. Nov 12, 2013

### ehild

|ψ(x)|^2 is the probability density of finding the particle around some specified x. So the probability that a particle is in a narrow range of width Δx around x is P = |ψ(x)|^2 Δx.
So P(xA) = Δx(-0.3)2=0.09 Δx and Pr(xB)=2Δx(0.12)2=0.0288 Δx, but you got the ratio correctly.

ehild

Last edited: Nov 12, 2013