In this 2nd year lecture, Mark Mezei writes down the Schrodinger equation for a particle moving in an arbitrary potential, before introducing the concept of stationary states and solving for them for the case of a particle in a box.
You can watch other lectures from the Quantum Theory course here: https://www.youtube.com/playlist?list=PL4d5ZtfQonW2RkYO1fbC3JBrRjMG2Pw-W
You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.