Considering degeneracy, Cohen-Tannoudji uses the symbol
½ k,l, m> [Coh, p.648, l.-
2]. In view of [Coh, p.782, l.- 7-l.-
3; p.783, l.- 6-l.- 5],
separation of variables makes it unnecessary to entangle ½
l,m> with the index k in most cases of interest. Even if we engage
½ l,m> with the index k, the result is not fruitful [Coh,
p.653, l.- 13-l.- 5].
Thus, to avoid complication, we had better leave out the index k (½
l ,m>: Mer2, p.238, l.-
7]) when discussing angular momentum.
The collision rate and the carrier density are two distinct sources of
temperature-dependence in conductivity. Defining the concept of mobility enables
us to separate from conductivity a factor whose temperature dependence reflects
only that of the collision rate [Ashc, p.563, footnote 1].
Using the general case can sometimes make the argument more flexible and
yield better results. However, this is not the case if we generalize the form
given in [Guo, p.212, (2)] to the form given in [Jack, p.97, (3.11)]. Jackson's
poor choice only makes his argument unnecessarily complicated. See his awkward
comments in [Jack, p.97,
l.14-l.15]. The theory of differential equations should talk about essence
rather than nonsense. "y1 and y2
given in [Guo, p.212, (4) & (5)] are linear independent solutions" is all
that need to be said.
Dichotomy: adopting a simple and natural point of view (the general viewpoint vs. the specific viewpoints)
[Born, p.38, l.-8], Born assumes that the incident
electric vector has a general form. Using [Born, p.39, (19)], he concludes that the
two component waves are independent of each other. In contrast, Hecht divides
his discussion into two specific cases [Hec, pp.113-115]. Using [Hec, (4.34),
(4.35), (4.40), (4.41)], Hecht also obtains the same conclusion. However,
Hecht's approach is more natural and less entangled than Born's.