Module 2 : Atomic Physics & Atomic Structure
Lecture 7 : Quantum Mechanical Treatment of One-Electron Atoms
Why Hydrogen ???
One electron atom and the simplest bound system in nature.
Referring to the adjacent Figure - 7.1, the proton (+ve Charge) is at the center and the electron (-ve charge) is moving around the center.
The attractive force between them is Coloumbic in nature and the potential is:
(7.1)
Where,
is the charge of the nucleus,
for hydrogen.
Figure - 7.1
Since it is a two body problem, we convert it to one body problem by introducing reduced mass:
Where,
and
are the masses of the electron and proton, respectively.
So, the total energy of the system = kinetic energy + potential energy
(7.2)
Here,
,
and
are the linear momenta and
is the total energy.
is the charge of the nucleus, 
for hydrogen.
and 
are the masses of the electron and proton, respectively.
, 
and 
are the linear momenta and 
is the total energy.