Physical Interpretation of the Angular Equation Solutions

Concentrating on the mathematical solutions of the Schrodinger equation, we can easily lose touch with the physical problem that is being considered. We will now recap the classical picture of the electron motion in an orbit around the nucleus so that we can try to relate the solutions found for the angular equation to this more tangible model. This will also allow the differences between the classical and quantum pictures of matter at the atomic scale to be highlighted. 

In the classical H-like atom the electron is bound by its electrostatic attraction to the positively charged nucleus. The potential energy of the electron at a distance r from the nucleus was quoted in atomic units in Equation (A9.4) in SI units we would have 

If this displacement takes place in the short time t, then we have the acceleration  

The differential of the angular displacement can be used to define an angular velocity  

The electron will sweep out 27t radians per revolution while it actually moves a distance of 27Tr, and so the angular velocity is related to the linear velocity via 

---