EM Wave Components for a Photon?

[LarryS]

Although mass-less, a photon, like any other quantum particle, has a frequency/wavelength associated with its energy/momentum. If we have a group of photons all with the same specific energy, then each photon can be represented by a little, complex-valued plane wave.

Photons are also EM waves and, as such, have (I assume) little Electric and Magnetic sine waves. How are those electric and magnetic (classical) wave components related to the above complex-valued plane waves?

Thanks in advance.

 

[tech99]

Although mass-less, a photon, like any other quantum particle, has a frequency/wavelength associated with its energy/momentum. If we have a group of photons all with the same specific energy, then each photon can be represented by a little, complex-valued plane wave.

Photons are also EM waves and, as such, have (I assume) little Electric and Magnetic sine waves. How are those electric and magnetic (classical) wave components related to the above complex-valued plane waves?

Thanks in advance.

Not sure what you mean by "complex valued"?

 

[LarryS]

Not sure what you mean by "complex valued"?

I was referring to QM wave functions having complex numbers for their values.

 

[A. Neumaier]

You are probably asking for the Riemann-Silberstein vector. See
http://arxiv.org/abs/1211.2655

 

[tech99]

I was referring to QM wave functions having complex numbers for their values.

Thank you. This is my engineering answer! If one takes the case of a pure CW (monochromatic) source of emission, then its radiated fields are sine waves and contain many photons. But if the wavelength is short, such as for light, we notice the quantum effects as noise modulation on the signal. We can think of the signal becoming more granular. As the wavelength becomes shorter the more the signal is modulated with noise. As the noise accompanies the signal as a form of modulation and is absent without it, it is similar to shot noise in a resistor - the noise caused by current flow. The noise modulates the signal both in amplitude and phase; this is due to the complex values of the quantum wave function, there being a quadrature component.

 

[sheaf]

Photons are also EM waves and, as such, have (I assume) little Electric and Magnetic sine waves.
Thanks in advance.

Note that if the field is in a photon number eigenstate (definite number of photons), it does not look like a classical EM plane wave field - for example the expectation value for the electric field is zero. If you want to build a field which looks like a classical plane wave, you end up with a coherent state - one in which there is not a definite number of photons.