Thermodynamics, Statistical Physics, and Quantum Mechanics

326 SOLUTIONS

we will get and which contradicts the assumption.

So the electrons are relativistic. Alternatively, we can use the result of

Problem 4.64,

the same as S.5.73.5.

b) The ground state energy of the system is given by the sum of energies of
all levels, which we may approximate by an integral. We calculate the total
energies of non-relativistic particles (neutrons and protons) and relativistic
ones (electrons) separately:

For 1-D electrons (see Problem4.64)

The total electron energy is