According to quantum mechanics, the energy levels for an particle with mass m (such as an electron) confined in a 1-dimensional box of length a is given by

En = n^2 (h^2/(8ma^2))

where h is Planck's constant and n takes integer values: n = 1,2,3...

a) What are the energies for the first 4 states (expressed in terms of E1)?

b) What are the possible distributions of of three particles such that E = 81E1?

Is (0, 0, 0, 0, 0, 0, 0, 0, 1, 0,...) an acceptable answer?

c) Find Ω for each of the acceptable states.

d) What is the probability of nding particle "A" in E1 for the distribution (1, 0, 0, 1, 0, 0, 0, 1, 0, 0,...)?

e) What is the probability of finding particle state in E1 for the acceptable distributions?