The lecturer is Professor Leonard Susskind and the video lectures are courtesy of Stanford University.
This course is an introduction to quantum mechanics. It covers just enough to get a decent grounding in the subject, and Professor Susskind uses simple examples to describe the fundamental difference between the classical and quantum descriptions of nature.
The following subjects are covered:
- quantum states and the nature of measurable quantities, called observables
- the spin of an electron
- how pairs of electrons are said to be entangled
- Bell's theorem and how it fails for the singlet state
- The two-slit experiment
- quantum entropy and the density matrix
- The evolution of quantum states and observables over time
- The notion of the Hamiltonian in quantum mechanics
States describing quantum mechanical systems are best described by vector spaces over complex numbers, in marked contrast to classical states, which are not vector spaces at all, but just sets of points in an abstract space.
So, you will need to know the basics of complex numbers and have a reasonable grasp of linear algebra (abstract vector spaces, matrices/operators, eigenvalues and eigenstates) in order to get the most out of the lectures.
Even so, each of these concepts are covered, albeit in the special case of vector spaces over complex numbers.
The good news is that only finite-dimensional spaces are used in this course.
This website has no connection or affiliation to either Stanford University or Professor Leonard Susskind.
This is one non-physicist's set of organised notes which, hopefully, may be of some use to others. Any errors in my notes are mine alone and readers should beware that they might not reflect the content of the lectures accurately.
I would very much appreciate all and any corrections, especially on any of the physics or mathematics, but I'm sure there's the odd typo or two!