Suppose that you have two basis in 2 different Hilbert spaces (each of them with dimension 2). Suppose that the vectors of the basis are (1,0) and (0,1 ), belonging to the Hilbert Space H1, and (1,0) and (0,1 ), belonging to the Hilbert Space H2. You want to obtain the tensor product among these vectors to create a new Hilbert space with dimension 4. For example, I want that the tensor product between (1,0) from H1, and (1,0) from H2 give me the vector (1,0,0,0) in (H1 x H2) and so on, in such a way that
(1,0) x (1,0)= (1,0,0,0)
(1,0) x (0,1)= (0,1,0,0)
(0,1) x (1,0)= (0,0,1,0)
(0,1) x (0,1)= (0,0,0,1)
where the "x" here would be the tensor product between the vectors on the original basis. In thyis way I can create the new basis in the new 4 dimension Hilbert space from the basis in the old two different Hilbert spaces with dimension 2. Somebody knows how can one define this operation? Or is there any operation in Mathematica that do this directly?
