Considered by the founders of

quantum mechanics to be, along with

the principle of superposition, the most

fundamental of the new theory's

concepts.

Commutation relations are usually written in brackets, but I will use {}.

{Xi,Pj}=i*hbar*kroneckerdelta_ij

i is the squareroot of -1, hbar is planck's constant divided by 2*pi, and the kroneckerdelta_ij is one when i=j and zero otherwise.

Xi and Pj in turn refer to the x,y,z components of both position and momentum.

The commutation relations show, in a concise format, how when measuring physical quantities on the order of hbar in magnitude, the eigenvalues of certain non-commuting observables may not be specifiable simultaneously.

Heisenberg's uncertainty principle is thus derivable from the commutation relations, which were themselves inspired more by Hamilton-Jacobi theory.