Here we illustrate a simple example of quantum commutator algebra using a one-dimensional quantum system. Let
be a function
of
. The three commutators
of
and of each of the functions
,
, and
may all be identified (to within the factor
) with the derivative with respect to
of these functions, but they are not the same operators. Indeed, by repeated application of the commutator algebra
rule
![]() |
(1) |
we get
In the same way
[1] Messiah, Albert. "Quantum mechanics: volume I." Amsterdam, North-Holland Pub. Co.; New York, Interscience Publishers, 1961-62.
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