||Operator Representations for Radial Wave Functions of Hydrogen-like Atoms
The author presents the operator formalism in dealing with radial wave functions of hydrogenlike atoms. The essential point rests upon that the radial wave functions can be derived by successively operating lowering operators on a radial wave function having a maximum allowed orbital angular momentum quantum number. This approach resembles the operator formalism that deals with a quantum mechanical harmonic oscillator. The results agree with the conventional coordinate representation method based upon power series expansion that leads to associated Laguerre polynomials. The operator formalism explicitly represents the mathematical constitution of quantum mechanical systems. In this article the author shows this feature by adopting radial wave functions of hydrogen-like atoms as an example.