# Reconciling quantum with classical mechanics

1. Jan 9, 2010

### physikerin

1. The problem statement, all variables and given/known data

The pendulum of a grandfather clock has a period of 1 s and makes excursions of 3 cm either side of dead centre. Given that the bob weighs 0.2 kg, around what value of n would you expect its non-negligible quantum amplitudes to cluster?

3. The attempt at a solution

I am very uncertain about this attempt. I know that a measurement of energy is guaranteed to yield a value that lies close to E=En where I think that En is given by En=(n + 1/2) hbarw. So I thought that I could calculate the potential energy at the highest point of the oscillation (by using the fact that T=2pi(L/g)^1/2 and working out how high the bob swings) and equate that to En and then work out n. The answer I got for that however was phenomenally large however (around 3.63*10 to the 32 or so) and while i know that n should be large I'm not entirely certain it should be quite so large.

Any suggestions?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution