Operator Realization of Radial- and Azimuthal- Differentiations Obtained by Using the Entangled State Representation

Abstract

We find Bose operator realization of radial-and azimuthal-differential operations in polar coordinate system by virtue of the entangled state |η representation, which indicates that |η representation just fits to describe the polar coordinate operators in quantum mechanics. The Bose operator corresponding to the Laplacian operation ∂ 2 ∂r 2 + 1for 2-dimensional system and its eigenvector are also obtained. Their new applications are partly presented.