A Hamiltonian with a tensor product - a few basic questions

[Thomas Brady]

I am given a hamiltonian for a two electron system $$\hat H_2 = \hat H_1 \otimes \mathbb {I} + \mathbb {I} \otimes \hat H_1$$
and I already know $\hat H_1$ which is my single electron Hamiltonian. Now I am applying this to my two electron system. I know very little about the tensor product aside from a few basic properties. How would I go about writing my hamiltonian $\hat H_2$ in matrix form? What exactly is the mathematical structure of the tensor product? What is the purpose of taking the tensor product with the identity?

Sorry, I know these are fairly vague questions, but any kind of help is appreciated.

 

[blue_leaf77]

Take a look at this http://mathworld.wolfram.com/KroneckerProduct.html.