I have read that in quantum mechanics, compound systems are constructed as tensor products.
But on page 177 of Griffith, for example, a two body wavefunction is introduced as Psi (x1,y1,z1,x2,y2,z2,t). (Six space dimensions plus time) This is clearly a direct sum, not a tensor product.
If this is correct, when do you use a direct sum and when do you use a tensor product?
Why isn’t the tensor product representing the two body system
Psi(x1x2,x1y2,x1z2,y1x2,y1y2,y1z2,z1x2,z1y2,z1z2,t) or something similar?
(nine tensor dimensions plus time). What am I misunderstanding?
And what are the tensor space dimensions?
Or how do these abstract dimensions relate to physical lab space dimensions?