# Particle in a Box

## Homework Statement

What is the probability, P, of locating a particle between x = 0 (the left-hand end of
a box) and x = 0.2 nm in its lowest energy state in a box of length 1.0 nm?

## Homework Equations

Probability = ∫ψ2dx
ψ = (2/L)1/2sin(n∏x)

## The Attempt at a Solution

ψ2 = (2/L)sin2(n∏x)
∫(2/L)sin2(n∏x)dx = 2/L [x/2 - (L/n∏x)sin(2n∏x/L)] from x = 0 to x = 0.2

I plugged in the numbers n=1 and L = 1 and got about 0.2.

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TSny
Homework Helper
Gold Member
ψ2 = (2/L)sin2(n∏x)
∫(2/L)sin2(n∏x)dx = 2/L [x/2 - (L/n∏x)sin(2n∏x/L)] from x = 0 to x = 0.2
Check the factor highlighted above. Note that this factor should have the dimensions of length.

TSny
Homework Helper
Gold Member
Not necessarily. The particle in a box is often covered in the introductory calculus-based physics course (usually in the 3rd semester of the course in the U.S.).

Check the factor highlighted above. Note that this factor should have the dimensions of length.
I still don't understand.

I may have wrote something wrong.
The part that you highlighted should be: (L/n∏)

I got the answer now, but by changing my calculator to radians when calculating sin(2n∏x/L). Am I suppose to use radian instead of degrees?

Yes you are... you are working with numbers here, not with angles... in this case the sine is just a function, and want an adimensional argument. While radians are a conventional unit for angles but are not a real units (you call radians to understand that you are speaking of angles but it is still a pure number), degrees are indeed an unit, so you can't use them here

Yes, well done, you're right, radians always for this sort of thing. Took me ages to get used to that.

Yes you are... you are working with numbers here, not with angles... in this case the sine is just a function, and want an adimensional argument. While radians are a conventional unit for angles but are not a real units (you call radians to understand that you are speaking of angles but it is still a pure number), degrees are indeed an unit, so you can't use them here
Ok...Thanks!