Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?

Vachaspati

Vladimir I. Man’ko, Giuseppe Marmo, F. Zaccaria

Marc Henneaux A

Eugene Paul Wigner

The commutator of the Hamiltonian with the operator corresponding to any physical quantity gives the operator which corresponds to the time derivative of that quantity. One can ask, hence, whether the postulate, that the quantum mechanical operators obey the classical equations of motion, uniquely determines the commutation relations. The answer is found to depend on the form of the Hamiltonian and is in the negative for a free particle and for the harmonic oscillator.

R. O'Raifeartaigh, Colm A. Ryan

The method of the complete set is used to study a generalized commutation relation. This commutation relation is of interest for two reasons. First, it is very similar to the commutation relations considered by various authors in connection with generalized statistics. Secondly, it allows us to investigate further a problem previously considered by Wigner, namely, Do the equations of motion determine the quantum mechanical commutation relations? '' (auth)