Schrödinger's Cormorant

6-8 ① We know that the probability of the particle being found somewhere between 0 and L equals 1 (because it must be somewhere. If there is constant probability density over the range of L, we can therefore say that the probability that the particle will be with in a range of length Δ will be given by:

(Δ / L) x 1

We have specified that x should be between 0.09L and 0.11L, which is a range of 0.02L. So the probability that the particle will be found in this range is given by:

(0.02L / L) x 1 = 0.02

② We could also have found this using the general method we learned in Chapter 5:

If the probability density is constant over the whole length L, we know that F(x) will just be a constant, c. We can normalise by requiring that

Hence cL = 1 and we can deduce c = 1/L.

③ We can, therefore, confirm the probability that the particle will be found between 0.09L and 0.11L by finding the definite integral:

Back to Question

Back to Chapter

Page updated

Google Sites

Report abuse