Thermodynamics, Statistical Physics, and Quantum Mechanics

32 PROBLEMS

Quantum Statistics

4.64 Fermi Energy of a 1 D Electron Gas

(Wisconsin-Madison)

Calculate the Fermi energy for a one-dimensional metal with one freeelec-

tron per atom and an atomic spacing of 2.5 Å atT= 0.

4.65 Two-Dimensional Fermi Gas (MIT,

Wisconson-Madison)

Consider a noninteractingnonrelativistic gas of N spin-1/2 fermions at

T= 0 in a box of areaA.

c) Qualitatively discuss the behavior of the heat capacity of this system

at low temperatures.

4.66 Nonrelativistic Electron Gas (Stony Brook,

Wisconsin-Madison, Michigan State)

Derive the relation between pressure and volume of a free nonrela-

tivistic electron gas at zero temperature.

The formula obtained in (a) is approximately correct for sufficiently

low temperatures (the so-called strongly degenerate gas). Discuss the

applicability of this formula to common metals.

Find the Fermi energy.

Show that thetotal energy isgiven by

a)

b)

a)

b)