Probability for particle in infinite square well

[pinkfishegg]

Homework Statement

A particle is confined between rigid walls separated by a distance L=0.189. The particle is in the second excited state (n=3). Evaluate the probability to find the particle in an interval of width 1.00 pm located at
a)x=0.188nm
b)x=0.031nm
c)x=0.79nm
What would be the corresponding results for a classical particle[/B]

Homework Equations

P(X)=abs(ψ(x)^2)dx
ψ(x)=(√2/L)*(sin(nπx/L)

The Attempt at a Solution

for part a
P(x)=(2/.189)*(sin(3π(.0188))/.189))^2=.28/m

I know the probability is just a matter of squaring ψ but my answer is way off. The got 2.63*10^-5 for part A. My first through was why does my answer have units of 1/m. I'm guessing i should multiply by dx. I thought this may be 1.00 pm but simply multiplying my answer by 10^-12 won't get the job done. Am i getting some variables mixed up here?

 

[JorisL]

What are the units of L? Are they in meters? Micrometers? Or even nanometers?

That is what you have to find out!

 

[pinkfishegg]

What are the units of L? Are they in meters? Micrometers? Or even nanometers?

That is what you have to find out!

oh its L=0.189nm

 

[JorisL]

Does that fix your problem?

When I figured it out (trial and error) I immediately got the right answer.

 

[pinkfishegg]

Does that fix your problem?

When I figured it out (trial and error) I immediately got the right answer.

Silly me i kept my calculator in radians instead of degrees. But anouther not is that the dx is actually something you need to multipy by, not just some kind of notation. was getting 2.6*10-2 until i realized i needed to multiply by 10^-12 m. thanks for the help

 

[JorisL]

Awesome.