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## 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 = ∫ψ

^{2}dx

ψ = (2/L)

^{1/2}sin(n∏x)

## The Attempt at a Solution

ψ

^{2}= (2/L)sin

^{2}(n∏x)

∫(2/L)sin

^{2}(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.

The answer is 0.05.