A system has a temperature of 290 K and a chemical potential of -0.2 eV. For a certain quantum state in this system, the energy per particle is -0.16 eV, and any number of particles (bosons) may occupy it.
(a) What is the value of C in the probability formula Pn = Ce^(-nβ(ε-μ)) (to three decimal places)?
(b) What is the probability that this quantum state contains zero particles?
(c) What is the probability that this quantum state contains one particle?
(1 + x + x^2 + x^3 + · · · = 1/(1 - x).)