Is the photon's wave function the same as an electromagnetic wave (light)?
No, wavefunction is not the same as an electromagnetic wave. However take a look at Jeff Lundeen's material including his semi-technical explanation of weak measurement: "We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory". He's basically saying wavefunction is something real. On that basis there aren't two different things there, so it is the same as an electromagnetic wave. Also see The Maxwell wave function of the photon by Raymer and Smith.
The first that I have been taught in Quantum Mechanics is the photoelectric phenomenon. Without analyzing it, it concludes that when we shine light at the circuit(roughly speaking), the work required to free electrons in the circuit is analogous to the frequency.
The analogy is shaking an apple tree. If you don't shake it fast the apples don't fall down. Even if you have a whole army of people shaking the tree slowly, the apples stay put.
Then nearly every textbook says that this is because "light is made of corpuscles each carrying an energy h*v , called photons"(p.11 from Zettili's Quantum mechanics book) implying the wave-particle duality.
I can see it here. It's somewhat misleading because the ν is the frequency. Photons are waves, not corpuscles. I know Wikipedia shouldn't trump a textbook, but have a look at the Photon article and search on corpuscle. It isn't found. Then search on wave. There's 71 matches. Also take a look at Einstein's paper. The word corpuscle isn't mentioned in the Wikisource translation, or in this one. Einstein says this:
"According to this picture, the energy of a light wave emitted from a point source is not spread continuously over ever larger volumes, but consists of a finite number of energy quanta that are spatially localized at points of space, move without dividing and are absorbed or generated only as a whole."
So, is light(EM waves) the same as the wave function of a photon? If not, then what is their exact connection?
It depends on what you think a wavefunction is. Jeff Lundeen thinks it's a real thing that can be measured in the laboratory. And since there aren't two different real things present, it is the same thing as the electromagnetic wave. But see Wikipedia:
"A wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality. The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical "space", and in this respect it differs fundamentally from water waves or waves on a string".
Many people will say it's something different. I side with Jeff Lundeen myself.
