I am trying to follow a course on quantum mechanics taught by Leonard Susskind on YouTube.
Link to video: https://youtu.be/JzhlfbWBuQ8?t=4886
At 1:21:30, he introduces the distinction between the way classical mechanics is formulated as compared to quantum mechanics. In classical mechanics all the states of a system are specified as points on a phase space diagram. In QM states are vectors in vector spaces. I am just confused about how in the example of the phase space diagram he drew, he had position on the vertical axis and momentum on the horizontal axis, yet the state was not considered a vector, even thought it is specified by vectors.
Can someone explain my misconception please.