I have been following Leonard Susskind's 'Theoretical Minimum' lecture series on quantum mechanics he made in winter 2012, and have, at least up to lecture 7/8, understood what he is doing - he has primarily been looking at systems of single spin 1/2 particles and pairs of them, examining phenomena such as entanglement along the way. I am happy with what a quantum state is, and how it can be represented as a vector. However, Susskind started to introduce the wave function to his lectures, and I suddenly became incredibly confused. He says the following: "The wave function of a system, in a particular basis, is the projection of the state onto the basis vectors" His equation for the wave function, ψ(a,b,c...), is: ψ(a,b,c...) = <a,b,c...|Ψ>, where |Ψ> is the state of the system. All I'm really asking for are examples of the wave functions for single and double spin 1/2 systems, simply so that I can understand what he is talking about. Thanks in advance.