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Isolation from Complexity in Mechanics

  1. Considering degeneracy, Cohen-Tannoudji uses the symbol 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 l,m> with the index k in most cases of interest. Even if we engage 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 ( l ,m>: Mer2, p.238, l.- 7]) when discussing angular momentum.

  2. 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].

  3. 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.

  4. Dichotomy: adopting a simple and natural point of view (the general viewpoint vs. the specific viewpoints)
        In [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.