A playlist on quantum spin
I am watching a playlist on quantum spin. The following are some of my thoughts about quantum theory. We live in three dimensional real world, real here means real number instead of complex number. From time to time, theories built on complex numbers seem simpler. For example, sine and cosine functions often are simpler when written in complex exponential functions. In quantum physics, however, complex functions become essential in the construction of the theory itself. This I don’t understand. Quantum spin is the simplest quantum phenomenon. Learning quantum spin may help me gain a foothold for further understanding. Spin is very simple. It is simply up and down. But its mathematical model is quite perculiar. It is a two dimensional complex number model. We live in a three dimensional real number world. Why can’t we build a model in a three dimensional real world? Specifically, there is 180 degrees between spin up and spin down in physical space. But spin up and spin down are orthogonal to each other in the mathematical model. This means spin up and spin down are 90 degrees apart in the mathematical model. Why the difference? I have learned a lot from watching the videos. But quantum physics is always a mystery to me. Episode 3
The up state corresponds to eigenvalue one. The down state corresponds to eigenvalue -1. Is there any intrinsic reason for that? It seems that the up state and the down state are not symmetric.
Why theta/2? Probability is square. By squaring, half angle doubles. This is probably the source of 1/2. Is it also connected to the relation between phase velocity and group velocity? Phase velocity is half of group velocity in electron movements in atoms.
Can we represent everything in R3 instead of C2? Try it out!
Episode 5
Work out the exact form of E. It should be related to theta. It should be theta/2. Work it out!
With quantum spin, we can work out an example of time evolution of spin. That is really helpful for me to understand spin. Before, I only learned about the stationary solution of the hydrogen atom.
In 26:30, he said that quantum spin is simpler than the classic one. However, it is possible that the quantum model is simpler. It did not model the part of wobbling. Think more about it.
Watch episodes 4 and 5 again.
Episode 7
Solve the Schrodinger equation myself. See where sigma comes from. Can we determine sigma for specific situation, such as hydrogen atoms?
In spin, we give probabilities for up and down spins. In real life, for an electron in an atom, would the probability of a certain state be one most of the time? Think more about it and its consequences.
In 38:40, the equation about B is only related to A, the magnetic vector potential. But B should also be related to electric current. Why it is not there.
Why magnetic potential is a vector while electric potential is a scalar?
I stopped at 51 minute. Should resume later on. Overall, I should repeat listening again.
Episode 8
I've finished watching this last episode. He really taught a lot. He said that he covered many of the fundamental ideas in quantum mechanics. I have to watch the whole playlist again later.
The following is the link to the playlist.
Another playlist on spin https://youtu.be/qICXIY5Dynk
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