- #1

Lily Wright

- 9

- 0

## Homework Statement

If a one-dimensional box is 1 nm long, what is the probability of finding the particle between the following limits?

(a) x = 0 nm and x = 0.05 nm

(b) x = 0.55 nm and x = 0.65 nm

## Homework Equations

ψ = (2/L)

^{½}sin(πx/L)

## The Attempt at a Solution

(I do chemistry and I'm really terrible at physics so apologies if this makes no sense) So that's the equation I was given. But then the probability is ψ

^{2}which = 2/L sin

^{2}(πx/L).

And to find the probability between x = 0.55 nm and x = 0.65 nm I need to integrate this between those values. So that's what I've done putting L = 1 (but it's in nm?)

^{0.65}∫

_{0.55}ψ

^{2}(x)dx and then I get (πx−(sin(2πx)/2))π + C and then the rest is pretty difficult to type out but I basically end up with an answer of 0.1796. Any help would be much appreciated.