Electron in a Uniform Magnetic Field (Larmor precession)

In this video I will explain what happens when an electron is in a uniform magnetic field, which gives rise to a phenomenon called Larmor precession. I will explain the procedure in details that don't appear in any books,


My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Introducing the problem
00:30 Magnetic dipole moment
01:25 Hamiltonian of this interaction
02:10 Example: constant B in z direction
03:25 Determining the energy
08:00 Determining the time dependance
10:40 The expectation value of Sx
17:20 The expectation value of Sy
21:20 The expectation value of Sz
24:48 Looking at the expectation value vector (here is where the angle appears)
29:30 Determining the constants a and b in terms of the angle
36:50 The larmor frequency