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I think everyone who has attended a lecture introducing second quantization appreciates what a pain it can be to compute expressions involving commutators or anticommutators with lots of operators.

As an example, it's a classic exercise to compute the commutator of the Hamiltonian in second quantization of electrons with operators such as the density operator.

I wonder if there is a software, or maybe addons for Mathematica, that can do these simple but time-consuming operations?

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These tools do exist, though I think it's common for Mathematica inclined students to write their own ;) The most recent one I've come upon is: http://nrgljubljana.ijs.si/sneg/

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