Quantum corrections from simplest symmetric ordering

Abstract

The simplest symmetric ordering rule was used to quantize a classical monomial p^m qⁿ in phase space. An integral form for the quantum operator is derived and shown to be similar to Weyl transform, which is applied when considering completely symmetric ordering. Quantum-mechanical expectation values for both a general class of classical functions and the free-particle time of arrival operator are computed. We show that the leading terms coincide with classical expectation value.