Assume you have a system consisting of two spinless particles. The state vector corresponding to such a product is denoted by . This, however, does not mean that every vector in E is a product vector, only that it can be written as a linear combination of product vectors. The inner product in E satisfies .
Tensor products occur whenever a system has two or more independent degrees of freedom.
The x, y and z dependence cannot, in general, be factored. Certain operators in are product operators . If there can be no confusion we write . The evolution operator may then be written as . A basis for the global system is .