Quantum Theory of Atoms
For a particle in a cubic or rectangular box, Cartesian coordinates are more appropriate and there are three quantum numbers (n1,n2,n3) needed to label a quantum state
similarly in spherical coordinates, there are also three quantum numbers needed
l= 0, 1, 2, …,n-1 => n values of l for a given value of n
m= -l,(-l+1),…0,1,2,…,l => 2l+1 values of m for a given l
n is the principal quantum number and is associated with the distance r of an electron from the nucleus
l is the orbital quantum number and the angular momentum of the electron is given by L=[l(l+1)]1/2 h
m is the magnetic quantum number and the component of the angular momentum along the z-axis is Lz = m h