accessible states and average values recall the energy levels of a one-dimensional harmonic oscillator with frequency w: 2 using hw as the unit of energy and measuring energy from the zero-point energy hu/2, the above levels can be written as en ξ n, n=0, 1.2, . . consider a fictitious one-dimensional system, where two noninteracting bosons are confined in a harmonic oscillator potential. noninteracting means that each boson can take any of the energy levels in eq. (2) independently of the other. the two bosons can be distinguished by their colour, red (r) and blue (b). the total energy of the system u is given by the sum of energy of the two bosons, uenr tenpnr+nb, where nr and np can take any nonnegative integer. (a) suppose that the total energy of the system is fixed to be u = 6, enumerate all the microscopic/quantum-mechanical states accessible to the system and evaluate the average value of nr、(nr) (b) now consider having three bosons in the system, which are distinguished by their colour, red (r), blue (b), and green (g). enumerate all the microscopic states accessible to the system for the total energy u 6 and evaluate(nr)