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I am a high-school student who recently finished the chapter on QM. I thought I completely understood it, but when I started to look back at what I’ve learnt, then suddenly, nothing really makes sense. And one of the things I find really really hard is the nature of electrons. My textbook mentions the Schrödinger’s theory and the Louise de Broglie’s hypothesis about matter’s waves; and the followings are what I currently understand about these two theories:

- De Broglie hypothesized that electron has a wave associated with it; that is, electrons are wave-like particles. We can describe an electron as a wave with the wavelength of λ=[itex]\frac{h}{p}[/itex]. And this has actually been tested by the electron diffraction experiment (that of Davisson & Germer)

- However, in Schrödinger’s theory, electrons in hydrogen atoms are described as particles; this is because the wave functions give us the probability of finding the electrons at a particle space in a particular time.

So my first question is that: Is an electron an actual wave (as de Broglie suggested)? or do we describe an electron as a particle in whichonlyits probability is a wave (as Schrödinger suggested)? In other words, when we say electron is a wave, then what is actually waving? The probability or the electron itself?

My second question is that: is there any intuitive ways of explaining the probabilistic nature of the universe and of the electrons in particular? I have not read Schrödinger’s derivations of his equations yet, so I really don’t know what’s out there.

Finally, as far as I know, the wave-particle duality hasn’t really been solved to a fully-satisfying extent. So my last question is that: Have there been any suggestions/hypotheses to how this wave-particle paradox can actually be solved? Or have we accepted that this wave-particle duality is actually the nature of the universe?

I know that a photon must be described as a particle with discrete energy [itex] E=hf [/itex] in order for us to explain the photoelectric effect. But when I asked my teacher: “where do we get the frequency ([itex] f [/itex]) from if we think of a photon as particle?”; then he replied: “you should think of photons as packets of waves instead”. So now I often think of photons as actual waves; however, for some reasons, these waves are being chopped up (i.e. divided) into packets with discrete energy. In this way, the wave-particle duality can be solved. Is it the correct way to intuitively think about the nature of the photons?

I am sorry if a similar thread has been posted here before; and if it is the case, can you please post the links to previous threads as well? Thank you so much in advance!

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# Wave-particle duality confusion

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