Ordering Ambiguity of Quantum Operators

Harkirat Singh Sahota, Kinjalk Lochan

Omar Mustafa, S. Habib Mazharimousavi

Ian T. Durham

Dehai Bao, Zhongyuan Zhu

In this paper, we establish three different types (type I, type II and type III) of parametrization of ordering ambiguity in operator formalism of quantum mechanics and discuss their nontrivial relations. Some commonly occurred bewilderment about ordering problem is made clear. We also show that the ordering ambiguity exists in path intergral formalism and the representation of the ordering ambiguity in the path integral formalism (discrete schemes) has a one-to-one correspondence with type II parametrization of the ordering ambiguity in the operator formalism. As a result, we show that to select a physically a misled attempt. Instead, we have to work with type III parametrization in the operator formalism to reduce the ordering ambiguity by physical requirements.

S. Habib Mazharimousavi

The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable values for the ordering parameters.

Mustafa, O, Mazharimousavi, S H

Ordering ambiguity associated with the von Roos position dependent mass (PDM) Hamiltonian is considered. A PDM-pseudo-momentum operator is introduced and generalized to d-dimensions. Intertwining our Hamiltonian with the von Roos d-dimensional PDM-Hamiltonian we observed that the so-called von Roos ambiguity parameters are strictly determined. The ordering ambiguity seems to be removed through our intertwining process, therefore.