Analytical Bra-Ket Tensor Products: Rules & Wolfram Mathematica

[limarodessa]

What are the rules of analytical – not numerical (matrix) entry of bra-ket convertion – operations on bra-ket, in particular – tensor product ?

For example – how in analytical form to do this:

U$|\Psi\rangle$

where:

U=I$\otimes$I

I=$|0\rangle\langle0|+|1\rangle\langle1|$

$\Psi=\frac{1}{\sqrt{2}}\left( {|0\rangle\otimes|0\rangle+|1\rangle\otimes|1 \rangle} \right)$

Also – is it possible to do it in the analytical (not numerical) form in the package “Wolfram Mathematica” ? [itex] [/itex]

 

[Matterwave]

The first operator operates on the first ket, and the second operator operates on the second ket independently.