1) Take a P.i.B wavefunction for an electron in an 8 nm long 1D box and consider dividing the entire length of the box into 8 equal segments of 1 nm each. Calculate the ratio of the probability of finding the electron in the first segment (x = 0 1 nm) to the probability of finding it in the fourth segment (x = 3 4 nm) for the n=1 state. The fact that this ratio is not equal to one is only true because of quantum mechanics.

2) Repeat the previous calculation for the n=41 state. What is the ratio?

3) What is the limit as n -> infinity? (what does this tell us about why a macroscopic particle moving about in a box with no potential has a uniform probability of being found throughout the box?)