Quantum physics deals with matter with wave properties. The behavior of a particle is described with a wave function, using Schrodinger's equation. The wave function is interpreted using probability because we cannot say exactly where a particle is. We judge where something is using generalized probability but cannot perform a measurement without the collapse of the wave function.
Actually let's talk about quantum physics. What is quantum physics? Quantum physics is what happens to physics when we give wave properties to matter. So matter no longer is allowed to sit in just one place like objects sitting there. We've got to have it spread out like a wave, and that's why we call it, given wave properties to matter.
Alright. So it's described by something called a wave function, alright, and so that's going to take the place of a position, a momentum and all those things. Instead of that we describe the behavior of a particle by its wave function. The wave function satisfies something called Schrodinger's equation which kind of takes the place of conservation of energy. You can think of it that way in quantum mechanics. Alright.
So, if we leave the particle alone, it behaves like a wave. So we're just sitting there letting the system do whatever it wants to do and it's described by its wave function. However, if we perform a measurement, suddenly we get something called the collapse of the wave function. So for example, if we've got a wave function that looks like that, and then we perform a measurement and we say, is the particle between these two green lines?
Well, I mean, we're performing a measurement. It either is or it isn't. So it doesn't get to say, oh, part of me is there and part, no. It doesn't get to say that. We're performing a measurement. We're asking is it or is it not? It cannot be both. And that is going to give us a probabilistic interpretation from quantum mechanics. So the wave function will give us probabilities. It will say alright. If you did that measurement 100 times, 6 times you're going to find that it was between the green bars and the other 94 times you're going to find that it wasn't.
Now, it's really a strange duality going on there because, if I were to leave it alone, it's kind of like part of it's inbetween and part of it isn't. But if I do the measurement, then it either is or it isn't. Whole thing is or whole thing is not. And so that's the weird part about quantum mechanics that makes people kind of fuzzy on it. Is that sometimes if you leave the system alone, it behaves like a wave and you can kind of think about it as partly being inbetween the green lines and partly being not. but if you do that measurement and you try to determine is it or is it not, then the answer is given probabilistically. You can't say before you do the experiment for sure how it will come out.
Alright. Now this is associated with something called quantization. Interestingly enough, quantization is something that only happens with waves. And it happens as a consequence of something called boundary conditions. So just like we have a standing wave in between two points, we can have the first harmonic, we can have the second harmonic, we can have the third harmonic but we can't have anybody inbetween. So we can't have something that goes like this. Because it doesn't work, it doesn't satisfy the boundary condition. So I've got a whole hump, two humps, three humps. I can't have one and a half humps. It doesn't work that way. So this is what leads to quantization. When I impose these boundary conditions on the wave function. And when I do that, I get energy quantization so that I can only have discreet energies. I also get angular momentum quantization in certain situations I'll get momentum quantization and that's what leads to these strange properties of quantum mechanics.