A Hamiltonian with a tensor product - a few basic questions

  • #1
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.
 

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