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### Multiply out product of sums

For a specific quantum mechanical problem I need to multiply out operators in order to calculate a trace by hand. For example I need a Hamiltonian squared with $H^2$. The Hamiltonian contains of a few ...
• 842
1 vote
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### Forming Kronecker products for "non-adjacent" vector spaces

In quantum mechanics, we often want to build operators acting on multiple particles by simply "Kronecker-ing" operators from the single-particle spaces. That is, if I have some matrix $A$ acting on ...
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1 vote
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### Convert, using the Pauli matrices, an $n \times m$ matrix of quaternions into a $2 n \times 2 m$ matrix with complex entries, and vice versa

I'd like to go between $n \times m$ matrices with quaternionic entries to (using, it would seem, the Pauli matrix conversion scheme) to $2 n \times 2 m$ matrices with complex entries, and vice versa. ...
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My goal right now is to implement some rules like linearity etc for noncommuting operators (arbitrary matrices etc). This is partly an exercise for me to understand MMA better so giving me a package ...
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Consider the following defined commutation relations: $$[\hat a,\hat a^{\dagger}]=1$$ $$[\hat b,\hat b^{\dagger}]=1$$ $$[\hat a,\hat b]=0$$ (where the usual algebra of commutators holds) Let us now ...