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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. ...
679 views

### 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 ...
632 views

### Outer product using the quantum mathematica package

I am using the quantum Mathematica package and am trying to do computations that require me to use the outer (tensor) products of Pauli matrices. I would define this as, for example, ...
1 vote
261 views

### 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 ...
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 ...