This is how Quantum Physicists communicate their ideas
Hi guys, so I wanted to make a video explaining some of the notation used by quantum physicists to describe their ideas. There is a reason why things are written the way they are, and it is interesting to see these reasons, in my opinion.
In the video we will see bra and ket notation, originally invented by Paul Dirac, which is used describe the wave function of a quantum state - essentially all the mathematical information we know about our quantum system, which is the part of the universe we happen to be studying.
Bra-ket notation uses a ket to represent a quantum state, with the ket being distinct from, but mathematically related to, the bra. The ket representing a quantum state can also be written as a superposition of possible results to a measurement. For example if our system is an electron, and we measure its spin, then the electron's state BEFORE we measure its spin can be written as a superposition of the possible results of a spin measurement - spin up and spin down. This superposition is mathematically written by adding states together. The numbers in front of each state are directly related to the probability of us finding our system in that state, upon measuring.
AFTER we make a measurement, the system collapses into ONE of the possible measurement results - we never actually find it to be in a superposition. There are other subtle effects that tell us that a quantum system can exist in a superposition of states, but upon measurement the system probabilistically collapses into one of the possible measurement result states. This is called the Collapse of the Wave Function.
We also see that quantum states can be very nicely described by vectors in an abstract mathematical space known as a Hilbert Space. The quantum states display certain mathematical behaviours that are very similar to those displayed by vectors in real space. Additionally, we can use the Hilbert Space to represent the state of any quantum system, even one in a superposition of states, with one single vector. Pretty neat right?
Now guys I know that there's a lot of background noise in this video - I'm really sorry about this, but after all I live with my family and they have every right to speak in their own homes lol. Next time I'll try to find a time when there isn't as much going on in the background, to make a video.
Let me know what kind of videos you want to see from me next!
Follow me on Instagram @parthvlogs - I'm going to be posting a couple of IGTV vlogs on there towards the end of the year. Until the next video, see you soon!
2 авг 2024
