I'm a chemist, so forgive me. I'm looking at Leonard Susskind's course on 'Quantum Entanglement', and we've just started on Qbits. Electron spin: we have two column vectors (1,0) and (0,1) to represent the two states, call them 'up' and 'down'.
The vector for the state for the electron being 'across' is given by a column vector (1/√2, 1/√2)
Here's my problem; why not (1/2, 1/2)? I know that vectors that represent physical states must be normalized, but where does the √2 come in?