We started by studying spin states of non-relativistic particles in quantum mechanics, which are described using something called a wavefunction, which is somewhat similar to a vector. We discussed how quantum properties differ from classical properties, how they can be measured (in particular, the so-called Stern-Gerlach apparatus), and how they can be described using wavefunctions. Importantly, the wavefunctions don't tell us an answer about the given property we look to measure, they only describe the probability of a given measurement: this is the key difference between quantum mechanics and classical physics.

Student has been working on problems regarding calculating probabilities and various mathematical aspects of the wavefunctions and related objects (specifically, the matrices that describe the spin basis). I also gave Studnet two special problems - one to compute something called a commutation relation for the spin matrices, which entailed a mini introduction to group theory (very closely related to the quantum concepts we've been studying), as well as a problem to compute the velocity of an electron in the lowest energy level of hydrogen. His solutions to these problems, as well as the numerous textbook problems undertaken so far, will be typeset in a final document which will comprise the product of his mentorship.

Student has a wonderfully curious mind and a natural intuition for'asking the right question.' He has been doing a good job working independently, reading the textbook as well as surrounding material related to the physics concepts. So far, we have not seemed to need to explicitly introduce many new mathematical technologies; his background is extremely solid, especially for his age.

One skill that is gradually developed as a physicist is to know which aspects of a given problem are the most important and which aspects are to be sidelined for a given calculation. This is something that I am seeing Student slowly progress in and by the time we finish the mentorship, I expect that skill to be better honed.

As mentioned above, the final deliverable is a typeset document of Student's solutions to the quantum mechanics and related mathematics problems. He seems to be on track to have completed at least 10 quantum problems and 3 (pure) mathematical problems however in our next meeting (this Friday, 8/18), I will stress the importance of staying focused on that goal and not getting too sidetracked with additional, interesting physics concepts that won't amount to contributing to the deliverable.