Understanding vector spaces in quantum mechanics

In this video we will explore the geometry of quantum states. While these are usually represented by vectors in Hilbert spaces, the true space is the projective space (the space of the "rays", one-dimensional sub-spaces). We will also see what is the difference between a complex vector space and a real vector space with double dimensions. Intro (0:00) States are "rays" (1:11) Real projective line (3:08) Real projective plane (8:44) Real vs Complex vector spaces (13:20) Complex projective line (18:40) Bloch sphere (23:40) Superposition (29:35) Time evolution (32:06) Physicality of superposition (38:16) Conclusion (45:00)