Merzbacher - Quantum mechanics, second edition, chapter 1 page 4,writes:(adsbygoogle = window.adsbygoogle || []).push({});

"A classically observable wave will result only if

the elementary wavelets representing the individual quanta add

coherently. "

Is this analysis correct?

The context is the following:

We may read (1.3) [ë = h/p] the other way around and infer that any

wave phenomenon also has associated with it a particle, or quantum, of

momentum p = h/ë. Hence, if a macroscopic wave is to carry an

appreciable amount of momentum, as a classical electromagnetic or an

elastic wave may, there must be associated with the wave an enormous

number of quanta, each contributing a very small momentum.

A classically observable wave will result only if the elementary

wavelets representipg the individual quanta add coherently.

For example, the waves of the electromagnetic field are accompanied by

quanta (photons) for which the relation E = hv holds. Since photons

have no mass, their energy and momentum are related by E = cp. It

follows that (1.3) is valid for photons as well as for material

particles. At macroscopic wavelengths, corresponding to radio

frequency, a very large number of photons is required to build up a

field of macroscopically discernible intensity. Yet, such a field can

be described in classical terms only if the photons can act

coherently. This requirement, which will be discussed in detail in

Chapter 22, leads to the peculiar conclusion that a state of exactly n

photons cannot represent a classical field, even if n is arbitrarily

large.

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# A classical wave as sum of many coherent quantum wavelets?

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