Normal ordering of the Dirac radial momentum operators and the power of radial coordinate operators by virtue of the IWOP technique (Q2773134)

The authors of this paper investigate the normal ordering expansion of the Dirac's radial momentum operator \(\hat P_r=(1/2)((\vec r/r)\cdot \vec P+\vec P\cdot (\vec r/r))\) \(=\) \(-i(\partial /\partial r+r^{-1})\) (\(\hbar =1\)), where \(r=(x^2+y^2+z^2)^{1/2}\). To derive the problem they make use of a technique known as integration within an ordered product (IWOP) of operators. Some operator identities of the power of radial coordinate operators, applicable in calculating expectation values in the coherent state, are discussed.