In summary, the conversation discusses the use of tensor product in the description of composite systems, as well as its application in single particle systems. The tensor product is an abstract representation that combines two independent spaces, vectors, or tensors into one, while preserving their linearity. This allows for a more intuitive understanding of the relationship between different systems.
#1
prabin
1
0
Can anyone answer me that why the description of composite system involve tensor product ? Is there any way to realize this intuitively ?
The tensor product is not only used for composite systems, even for a single particle moving in space the 3d base kets are built as a product of 1d kets
As I see it, the tensor product is an abstract formalization of the following fact: Let ##\psi(x_{1,}x_{2})## be a two-particle wave function and ##{\phi_{n}(x)}## an orthogonal basis of functions for the one particle Hilbert space ##L^{2}## (say, the Hermite polynomials). Then you can write ##\psi(x_{1,}x_{2})## as a linear combination of functions of the form ##\phi_{n}(x_{1})\phi_{m}(x_{2})##. If we write this using an abstract vector, we are basically defining a tensor product.
#3
Structure seeker
112
42
The tensor product is the mathematical respresentation of two independent spaces, two independent unit vectors/kets or two independent tensors to be viewed as one. The context is linearity, and the tensor product preserves the linearity of both factors in such a way that the restriction to one of both (via the trace over the other) returns the original vector/ket/space/tensor.