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Merzbacher - Quantum mechanics, second edition, chapter 1 page 4,writes:
"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.
"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.