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 \(\frac{\partial^{2}}{\partial r^{2} }+\frac{1}{r}\frac{\partial}{\partial r}+\frac{1}{r^{2}}\frac{\partial^{2} }{\partial\varphi^{2}}\) for 2-dimensional system and its eigenvector are also obtained. Their new applications are partly presented.
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