The function of terminology must be consistent in similar models (e.g.
waves). Suppose n_{I} < n_{T} and E is parallel to the plane of incidence. The reflected wave in [Cor, p.564, Fig. 30-6] and that in [Hec, p.116, Fig. 4.41] have different phases. This is because Corson thinks that E_{R} and E_{I} have the same phase if E_{Ix} E_{Rx} > 0 [Cor, p.560, Fig. 30-3], while Hecht thinks that the incident light is like a walking person whose left hand represents the direction of E and that E_{R} and E_{I} will have the same phase if its left hand still represents the direction of E after it bounces back from the interface [Hec, p.114, Fig, 4.40] . If we consider the system alone, it will be difficult to determine which of these two opposite views on phase shift is more appropriate. Now let the incident angle be 0^{o}. If a wave goes from a light string to a heavy one, the reflected wave will change phase [Hall, p.309, Fig. 17-15]. Thus Hecht's opinion on phase shift [Hec, p.118, Fig. 4.40(b)] is not consistent with this simple model. Therefore, I agree with Corson's opinion on phase shift.
Given a theory. When we make an assumption for definiteness, we must
justify that the assumption is consistent with the theory. Different
viewpoints may result in different appearances of a formula. In [Wangs, p.412, Fig. 25-9], we assume E_{i}, E_{r},
E_{t} are all directed out of
the page. Will this
assumption cause inconsistency?
It will not. This is because the title of [Wangs, §23-2]
reduces the various electrical fields to two directions and we are allowed to use a minus sign to represent the direction
opposite to that we assumed.
For example, the minus sign right next to the first equality sign in [Wangs,
p.413, (25-39)] reveals the fact that E_{r} is actually
directed into the page [Wangs, p.414, l.10].
Both [Wangs, §23-2] and [Wangs,
§23-3] should apply to the case of normal incidence
[Wangs, p.416, l.-21-l.-17].
However, [Wangs, p.416, the first equality of (25-50)] differs from [Wangs,
p.413, the first equality of (25-33)] by a minus sign. This is because [Wangs,
p.412, Fig. 25-9] and [Wangs, p.415, Fig.25-12] have different starting
points. The latter takes the opposite directions of E_{r} and E_{i} into account,
while the former does not.
Consistency requires that one make the difference between two statements
compatible by establishing a relationship between the two [Eis, p.99, l.25-l.34;
p.101, l.13-l.14].
Resolution of the discrepancy between theory and experiment makes the
turning point in the development of a new theory [Eis, p.13, l.-24-l.-22].
[Eis, p.13, Fig. 1-8] prompts Planck to propose his conjecture [Eis, p.13,
(1-19)]. He then tries to derive [Eis, p.13, (1-19)] by using [Eis, p.14,
(1-21)], a procedure that establishes the equipartition law. Planck finds that
Ē » kT
when DE is small and Ē » 0
when DE is large if energy E is treated as a
discrete quantity instead of a continuous one [Eis, p.14, l.-10].
The two determinations of Planck's constant h, using completely different phenomena and
theories, are in good agreement [Eis, p.31, l.-19].
In [Coh, p.653, (C-40)], Cohen-Tannoudji defines the phase of
ïk,j,m>. In [Coh, p.653,
(C-41)], he redefines the phase of ïk,j,m>. However, Cohen-Tannoudji fails to prove the consistency of the two
definitions. [Mer2, p.240, l.22] shows that the two definitions are consistent.
A random sign assignment is unacceptable even if it may lead to the correct final answer. A sign assignment
should be consistent throughout the book. If H_{r0}/H_{i0}= -Γ
[Sad, p.447, l.12], then the sign assignment will not be consistent with the usages
in [Sad, (10.31), (10.72) and (10.74)]. Therefore, H_{r0}/H_{i0}
should be Γ.
[Dit, pp.95-96, §4.A.9, & p.96, l.-6-l.-4]
essentially say that the following two operators do not commute:
Operator A_{1}: A_{1}(f) = the real part of
f.
Operator A_{2}: A_{2}(f) = the Fourier transform of f.
Why does the semiclassical analysis of [Ashc, chap.12] reduce to the Sommerfeld free electron theory of [Ashc, chap.2] when applied to the transport properties of alkalis
[Ashc,
p.287, l.2-l.4]?
Answer. alkalis [Ashc, p,287, Fig. 15.3]; noble metals .
Compare the results of the semiclassical model with the results of the Sommerfeld free electron model when we apply them to the transport properties of
noble metals.
Sameness [Ashc, p.289, l.1-l.9; Fig. 15.4].
Differences [Ashc, p.290, Fig. 15.5, necks exist; p.292, Fig. 15.7, there
are many types of orbits].
(Maxwell generalizes Ampère's law by
breaking through its inconsistency in the special case [of steady state]) Ampère's law [Jack, (6.1)(ii)] is not consistent with
the continuity equation [Jack, (6.3)] for time dependent fields. Maxwell breaks through the inconsistency
by using Coulomb's law to replace J with J + ¶D/¶t.
This generalized Ampère's law [Jack, (6.5)]
becomes consistent with the continuity equation [Jack, (6.3)] for time dependent
fields.
From a formal derivation to its internal consistency
Polarization charge densities
Polarization charge densities are derived from comparison of formal patterns [Wangs, p.143,
(10-6), (10-7) & (10.8)].
The physical derivation of polarization charge densities ([Fur, p.62, Fig. 2.2]; imitate the proof given in [Fur, p.64, l.1-l.7]).
Internal consistency:
Polarization charge densities satisfy
the boundary conditions [Wangs, p.145, l.3-l.5].
The total polarization charge is zero [Wangs, p.145, (10-13)].
Magnetization current densities
Magnetization current densities are derived from comparison of formal
patterns [Wangs, p.214, (20--9); p.315, (20-10)].
The physical derivation of magnetization current densities [Fur, p.64, l.1-l.7].
Internal consistency:
Magnetization current densities satisfy
the boundary conditions [Wangs, p.316, (20-12)].
The total magnetization current is zero [Wangs, p.317, l.5].