A passage on pages 346-347 in AShcroft and Mermin

[MathematicalPhysicist]

There's a passage on pages 346-347 which I don't understand.

They write:

When $\epsilon_1$ is exactly $\epsilon_F$, conditions (17.61) and (17.62) can only be satisfied if $\epsilon_2$, $\epsilon_3$ and $\epsilon_4$ are also all exactly $\epsilon_F$.

where the conditions are:
$$(17.61)\epsilon_2 <\epsilon_F, \epsilon_3>\epsilon_F, \epsilon_4>\epsilon_F.$$
$$(17.62)\epsilon_1+\epsilon_2=\epsilon_3+\epsilon_4$$

Well, obviously when all of the $\epsilon_i$'s are exactly $\epsilon_F$ then condition (17.61) isn't satisfied.

Perhaps they wrote something and meant something else... what do you think?

 

[mjc123]

Do you think the signs in 17.61 should be ≤ and ≥? Then it would work.

 

[MathematicalPhysicist]

Do you think the signs in 17.61 should be ≤ and ≥? Then it would work.

Obviously.