What is the Frequency in Einstein's Quantum Expression?

[exmarine]

Einstein’s discovery that a photon has a finite quantum of energy proportional to its discrete frequency, and the representation of that photon as a wave packet, gives me a problem.
E = h ν
The photon packet waveform surely must have a beginning and an end? It is probably continuous, etc.? The transform of such a packet waveform, whatever its precise shape, must contain many frequencies in order to “localize” the photon between its beginning and end. So what is the frequency in Einstein’s quantum expression?
Any thoughts are appreciated.

 

[vanhees71]

Right. A photon cannot be described in any way as classical particles nor as classical field. They are described by a quantized massless field with spin 1. There is, e.g., not even a welldefined position operator as for massive-particle fields.

You are also right in saying that a true one-photon Fock state, i.e., one that is normalizable to 1 is a wave packet and thus has a finite energy and momentum uncertainty. The plain-wave "states", i.e., energy-momentum eigenstates are generalized states in the sense of distributions, which becomes clear by the fact that they are only normlizable "to a $\delta$ distribution":
$$\langle \vec{p},\lambda| \vec{p}',\lambda' \rangle=\delta^{(3)}(\vec{p}-\vec{p}') \delta_{\lambda \lambda '},$$
where $\lambda \in \pm 1$ denotes the helicity of the single-photon state.

 

[Simon Bridge]

So what is the frequency in Einstein’s quantum expression?
Any thoughts are appreciated.

... it's the one that was understood as the frequency of the incoming light in his day. The frequency in the classical electromagnetic wave model.
see also

$E=h\nu$ shows how the idea of light coming in a lump is related to the idea that light comes in waves - what we've been calling "frequency" up to then is in fact "energy". Just like $E=mc^2$ shows that what we've been calling "mass" is also energy.


... as you see from vanhees71, there is, now, a more consistent description.