Re: Is photon a wave packet ?

[Brian Whatcott <inet@INTELLISYS.NET>]

At 10:36 5/15/02 +0800, you wrote:
> Hello friends,
>
> >I have two questions.
> >One, if a single photon has the property of wave?
> The single photon means an excited atom emits a single photon.
> >Two, if a single photon is a wave packet? i.e. if a single photon has
> >a width of frequency, but not monochromatic?
> In quantum field theory
>
>                     2
>             /       _
>             |       \
> A_{\mu}(x)= | d^3 k /  (a_{k,i} A_{\mu}(k,i;x) + a*_{k,i} A*_{\mu}(k,i;x)
>             |       -
>            /       i=1
>
> Here creation operator a_{k,i} creats an single photon with
> polarization i and frequency k. Thus for a single photon, it must be
> absolutely monochromatic. While for wave packet, it is a fourier
> expansion of variable frequency, may be k+-dk. For a wave packet the
> frequency has a width dk, but not a define and single freqency.
>                            |
>                          | | |
>                        | | | | |
>                      | | | | | | |
>                      | | | | | | |
>                     || | | | | | ||
>                     || | | | | | ||
>   _______________________________________________________
>
>                    k-dk    k      k+dk
> >From this point of wiew, one may say that a single photon is not a
> packet. That is why I asked if a single photon is a wave packet?
>
>
>
> --
> Best regards,
>  Qiang

I will respond with a counter example which you will readily accept.
I begin with a radio frequency source which is slaved to a traceable
frequency standard.
I will claim that this continuous say 1MHz source is monochromatic.
I then chop a narrow pulse from this standard signal, consisting of ten cycles
commutated on the zero crossings.
I see that the creation operator I used creates a pulse of known phase from
a monochromatic source. It is far from monochromatic, you will agree.

Take home message. Models are not reality.