Probability of finding a particle in a 1D Box

[scottnoplot]

Homework Statement

Determine the probability of finding a particle in a 1-D box of size L in a region of size 0.01L at the locations x = 0, 0.25L, 0.5L, 0.75L and L when it is in its ground state. As percentages

Homework Equations

[tex]\Psi[/tex](x)=[tex]\sqrt{\frac{2}{L}}[/tex]sin([tex]\frac{nxPI}{L}[/tex])
P=[tex]\Psi[/tex](x,t)^2

The Attempt at a Solution

I'm not even sure if I've got the right equations there, I've tried loads of different ways of doing this and cannot get the right answers, which are 0%,1%,2%,1%,0%

Cheers

 

[Mulder]

ok, finding probabilities means integrating the probability density - P=|[tex]\Psi[/tex](x,t)^2| - over parts of the box

try integrating over the whole box first, what does this give you?...

 

[scottnoplot]

ok, finding probabilities means integrating the probability density - P=|[tex]\Psi[/tex](x,t)^2| - over parts of the box

try integrating over the whole box first, what does this give you?...

[tex]\int[/tex]|[tex]\Psi[/tex](x,t)^2| = |[tex]\Psi[/tex](x,t)^3| /3

I think that's right.

 

[cpt_carrot]

[tex]\int[/tex]|[tex]\Psi[/tex](x,t)^2| = |[tex]\Psi[/tex](x,t)^3| /3

I think that's right.

Your answer cannot be a function of x, since you are integrating over x. Try substituting your expression for [itex] \Psi(x) [/itex] from your first post before you integrate.

 

[Zhivago]

You need to integrate |psi^2| from x=0 to x=0.01L , from x=0.245L to 0.255L, etc

Try to plot psi, |psi^2| and the integral of |psi^2| from 0 to x (remember that the integral is the probabilty of finding the particle in the limits of integration...)

 

[scottnoplot]

Thanks guys, got a bit of extra help and the penny has dropped now. cheers