Formulation of the Schrodinger Wave Equation for Hydrogen-like Atoms

Formulation of the Schrodinger Wave Equation for Hydrogen-like Atoms 

It can be shown that the second form of motion is mathematically equivalent to the movement of a hypothetical particle, with reduced mass /I, about a fixed point. The reduced mass is given by the formula  

The positive charge on the nucleus is equal to Ze, where Z is the atomic number of the atom, and the electron is attracted towards this charge with a force given by the inverse square law  

Figurie 6JZ Diagram of the hydrogen atom the relative movements of the proton and electron about the centre of mass (b) the mathematical equivalent of a particle of mass fi moving about a fixed point 

The replacement of the relative motion of two particles with that of a hypothetical particle of mass fi, knovm as the reduced mass is quite general, and has already been used in the description of the harmonic oscillator (Section 4.2.1) and the rotation of a diatomic molecule (Section 5.2.5). 

---