I What is difference between EM wave and EM field?

[fxdung]

They say wave function is different to quantum field. Then what is the difference between EM wave and EM field?(By the way :Is that EM wave the wave function of photons?).It seem to me EM wave is the wave of EM field?

 

[hilbert2]

If the EM field is static, like around a stationary electric charge, then it's definitely not something you'd call a "wave". And a time-evolving EM field can be seen either as a single object or several sine-form waves of different wavelengths added together. That allows determination of the spectrum of EM radiation, i.e. how much of each wavelength is contained in the field measured by some device. This doesn't have anything to do with quantum mechanics, yet.

The term "wave function" is a bit misleading, because the time-dependent Schrödinger equation is not an actual wave equation like that describing the propagation of an EM wave in vacuum. Its solutions just have some wave-like properties because it's a diffusion equation with complex multipliers.

 

[Demystifier]

It seem to me EM wave is the wave of EM field?

That's correct.

 

[fxdung]

Then what is the wave function of photons?

 

[hilbert2]

Then what is the wave function of photons?

The time dependent Schrödinger equation describes a non-relativistic massive particle and its wave function. A photon has no mass and always moves at speed of light so it can't be that.

 

[PeroK]

They say wave function is different to quantum field. Then what is the difference between EM wave and EM field?(By the way :Is that EM wave the wave function of photons?).It seem to me EM wave is the wave of EM field?

That question is a complete muddle of terminology from different theories: non-relativistic QM, classical EM, QFT, QED.

What are we talking about here?

 

[Delta2]

Then what is the difference between EM wave and EM field?

As @PeroK very successfully said you are mixing up different theories of physics. My answer would be within the theory of classical electromagnetism:
From Maxwell's equations which are the cornerstones of classical electromagnetism, we can infer that the electric and magnetic fields when they are time varying they obey the wave equation (see Inhomogeneous electromagnetic wave equation - Wikipedia ), therefore we can simply say that an EM wave is nothing more than a time varying EM-field.

 

[fxdung]

What about in stand point of QFT?

 

[Demystifier]

Then what is the wave function of photons?

@vanhees71 will tell you that there is no wave function of the photon. I will tell you that it is the Fourier transform of the 1-photon probability amplitude in the momentum space.

 

[vanhees71]

Define "1-photon probability amplitude in the momentum space"!

 

[Demystifier]

Define "1-photon probability amplitude in the momentum space"!

The most general 1-photon state can be written in the form
$$|\psi\rangle=\sum_{\lambda=1}^2 \int d^3k \, c_{\lambda}(k)\hat{a}_{\lambda}^{\dagger}(k)|0\rangle$$
where $c_{\lambda}(k)$ is an arbitrary function normalized so that $\langle\psi|\psi\rangle=1$. The usual Born rule implies that $c_{\lambda}(k)$ is the 1-photon probability amplitude in the momentum space.

 

[vanhees71]

Fine, and the Fourier transform is also fine, but that's not a "wave function" of a photon but a single-photon Fock state. I think to talk about "wave functions" in relativistic QT is misleading. You run in all kinds of trouble as the founding fathers of relativistic QM. I'd not recommend to study a textbook like Bjorken and Drell vol. 1 for students of the 21st century, when learning about relativistic QT but start right away in the formulation in terms of relativistic QFT.

 

[Demystifier]

but that's not a "wave function"

Well, it's a function and it's wavy.