Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• Show that for a degenerate gas of fermions at T = 0, the average energy per particle and the Fermi energy EF (the energy of the highest occupied states) are related by 〈E〉 = (3/5) EF. [Hint: Avoid writing any messy constants in your calculation, by noting that we can write

where and C is a constant that you don’t need to know because it cancels.]