De Broglie wavelength and how it leads to the wave function

Question

From what I know, de Broglie derived the wavelength equation using Einstein's $E=mc^2$ and the Einstein-Planck equation $E=h\nu$. My teacher explained this by saying an electron literally moves in wave form. This I thought was absurd. How does the Einstein-Planck equation used for light lead to a probability function of an electron? Doesn't that imply that an electron wave is just like a photon wave? I want to know how the de Broglie wavelength is different from the classical notion of wavelength.

I'm new to all the abstract concepts of quantum physics.

Answer 1

You’ll never get an easy answer on this one, even from the best physics profs. We all know they have wave behaviour because of the double slit experiments. All good high school teachers and university profs will focus on the particle, i.e. photon, electron, buckyball etc, and this is historical but a modern QM physicist will tell you the particle is dumb and it is much more important to focus on the field, I. E. the EM field.

All, all, all interactions of matter/ photons that we observe with our eyes, detectors, ccds etc is due to the EM field. Like an electron about to be emitted, the EM field is already active and resonant (likely the electron is initially resonating) causing “virtual” waves in the apparatus. Similar to photons pathways are preferred that are full wavelength multiples, hence the interference.