(kardar problem 7.2) generalized ideal gas: consider a gas of non-interacting identical (spinless) quantum particles with an energy spectrum ε p/ s, contained in box of volume v in d dimensions (a) calculate the grand potential sn--6bt inqη, and the density n = n/v , at a chemical potential μ. express your answers in terms of s. d, and f (z), where exp(βμ), and where η = +1,-1 corresponds respectively to the be, fd cases (b) find the ratio pv/e, and compare it with the classical result obtained previously. (c) for bosons, find the dimension de(s), below which there is no bose-einstein con- densation. is there condensation for s = 2 at d 2?