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Re: [Phys-L] electron location & wave function



On 04/16/2013 05:07 PM, Larry Smith wrote:
I'd also be interested in your elaboration on the inconsistent ways
"quantum of a field" is used.

Concept #1: A photon is a localized wave packet. Typically one imagines
a Gaussian envelope on top of a running-wave carrier, as in this picture:
http://www.av8n.com/physics/wavefunctions.htm#fig-running-wave-packet

As such, the photon is necessarily *not* monochromatic.


Concept #2: A photon is an excitation of a particular mode of the EM
field. Each mode of the field is a harmonic oscillator, and as such
the energy states are quantized, and the quantum number N is called
the photon number.

As such, the photon is necessarily monochromatic.

===================

In a separate subthread:
-- some people talk about the dichotomy between elementary particles and waves.
-- some people talk about the dichotomy between elementary particles and fields.

Obviously waves and fields aren't quite the same thing. Roughly speaking,
I would say that the waves are the /excitations/ of the field.

Most importantly, I reckon that neither of those dichotomies is worth
worrying about. There's just stuff. The stuff is what it is and does
what it does. The stuff doesn't care whether you call it a particle or
a field or a wave or whatever.

Feynman, in the Messenger Lectures "The Character of Physical Law" was
emphatic that quantum mechanical stuff is
a) not like classical particles, and
b) not like classical waves.

The QM waves are different from classical waves. For starters, the ordinate is
a complex number rather than a real number. However, I consider these differences
to be relatively superficial. Intuition about classical waves can be put to good
use, with a few modifications.

In contrast, intuition about classical particles does not, so far as I can tell,
tell us much of anything about QM that the wave picture did not already tell us.

So I say start with the fields. Waves are excitations of the fields. You can
ride this horse a very, very long ways.

If there is some observable result you think cannot be explained using this approach,
please say what it is, so we can discuss it.