By Paul Roman

ISBN-10: 0201064952

ISBN-13: 9780201064957

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**Additional info for Advanced Quantum Theory**

**Sample text**

5) for running waves, but it fails in the case of standing waves. Then the time averaged Poynting vector vanishes; nevertheless, a photographic plate is blackened at the positions of the maxima of the electric field strength, an effect known from Lippmann color photography. 20 Basics of the classical description of light called intensity: 11 2T I (r, t) = t+ 12 T E2 (r, t ) dt . 10)). 9) 0 and we note that f (−ν) = f ∗ (ν) because E is real. 5) for the intensity reduces to the simple form I (r, t) = E(−) (r, t)E(+) (r, t).

We require the 34 Quantum mechanical understanding of light field to be periodic in all three spatial directions with a (large) period length L. The aforementioned resonator volume is replaced by a “periodicity cube” with an edge length L. The modes selected by the boundary conditions are monochromatic running plane waves differing in propagation direction, frequency and polarization. ) Because the length L does not have any physical meaning, we can eliminate it by calculating first with a fixed L value and then, once we have the final result, performing the limit L → ∞.

This is the fundamental concept of classical statistics: we are satisfied with the use of probability distributions for the variables we are interested in, not from fundamental but purely practical reasons. The necessity is even turned into an advantage in the case of many-particle systems, for instance a gas; what would be the benefit of an absolutely detailed description of, say, 1023 particles even if our brain could digest such an overwhelming amount of information? We can make the rather general statement that the uncertainty of classical physics is equivalent to a certain amount of ignorance with respect to an otherwise well defined situation.

### Advanced Quantum Theory by Paul Roman

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