... address.^1.1

Reprinted in: Boorse, H. A., and L. Motz, 1966: The world of the atom. Basic Books, New York, 1873 pp.

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... as^2.1

The notation $\exp (x)$ is just another way of writing the exponential function $e^x$. We prefer this way because it is prettier when the function argument is complicated.

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... relativity)^3.1

Gravity waves in the atmosphere are vertical or slantwise oscillations of air parcels produced by buoyancy forces which push parcels back toward their original elevation after a vertical displacement.

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... Broglie^9.1

See Louis de Broglie's 1929 Nobel Prize address, reproduced in Boorse, H. A., and L. Motz, 1966: The World of the Atom, Basic Books.

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... versa.^9.2

This group velocity calculation ignores the possible dependence of index of refraction on wavenumber. If $n$ is a function of $k$, the calculation is more complicated, but the principle is the same.

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... total.^9.3

In advanced mechanics the total momentum is called the canonical momentum.

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... momentum.^11.1

The back pressure of the gas outside the system on the gas inside the system is negligible once the gas exits the nozzle of the rocket engine. If we took the inside of the combustion chamber to be part of the system boundary, the results would be different, as the gas pressure there is non-negligible. At this point the gas is indeed exerting a significant force on the rocket. However, though this viewpoint is conceptually simpler, it is computationally more difficult, which is why we define the system as we do.

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... mass.^12.1

In the presence of a potential momentum we would have to distinguish between total and kinetic momentum. This in turn would lead to a distinction between total and kinetic angular momentum. We will assume that no potential momentum exists here, so that this distinction need not be made.

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... momentum.^15.1

In advanced mechanics, $\mbox{\boldmath $\Pi$}$ is called the canonical momentum.

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... energy^15.2

In relativity, the quantity $E - U$ is actually equal to the kinetic plus the rest energy. This quantity ought to have a separate name but it does not.

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... other.^15.3

We use the symbol $\mbox{\bf p}$ for kinetic momentum here. However, in collisions we assume that the potential momentum and energy are only non-zero when the particles are very close together. Thus, when the particles are reasonably well separated, the distinction between kinetic and total momentum is unimportant.

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... circulation^18.1

The terminology comes from fluid dynamics where the concept is used with the fluid velocity field. The idea of circulation is so useful in fluid dynamics that it seems worthwhile to generalize it to vector fields in other areas of physics.

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... them.^19.1

Many of the ideas in this chapter were taken from Aitchison, I. J. R., and A. J. G. Hey, 1989: Gauge theories in particle physics. IOP Publishing, 571 pp.

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... pairs.^21.1

Actually, lepton conservation is even more restrictive, with conversion between electrons, muons, and tau particles being apparently forbidden. However, recent work shows that electron, muon, and tau neutrinos convert into each other on slow time scales. We also know from this work that neutrinos have small, but non-zero mass. The implications of these results are still being explored by the physics community.

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... law.^23.1

An empirical law is one which we cannot justify in terms of the fundamental principles of physics, but which is observed to be true in a wide variety of situations.

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... approximation^24.1

To derive the Stirling approximation note that $\ln (N!) = \ln (1) + \ln (2) + \ldots + \ln (N)$. This sum can be approximated by the integral $\int_1^N \ln (x) dx = N \ln (N) - N + 1 \approx N \ln (N) - N$.

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