As may be expected form the earlier discussion of a particle in a three-dimensional box, three quantum numbers emerge form the application of the boundary conditions, namely that is single valued, continuous and finite. The energy E of Eq 4.5 depends explicitly on n and the quantum numbers ml and l explicitly appear only in Eqs. 4.3 and 4.4.
The quantum numbers are
n, where n =1, 2, 3…..
l, where l = 0, 1, 2, …..,n-1
ml , where ml = l, l -1, l -2,….., 0, …., -1, -2……-l
The energy of the electron in a multielectron atom is expected to depend on the combination of all three quantum numbers, but in view of the fact that the hydrogen atom has only one electron, the energy depends only on the quantum number ‘n' which is therefore called principal quantum number. The quantum number ‘l ' is called the angular momentum quantum number and determines the angular momentum and hence the rotational kinetic energy of the electron. Since the angular kinetic energy cannot exceed the total energy of the electron, the values which ‘l ' can take, are restricted from above by the values of ‘n'. The third quantum number, ml is called the magnetic quantum number. For l > 0, the angular momentum can project with different components in a given direction.
The number of projections is given by 2l +1. The range of values which ml can take is governed by the value of ‘l '. The electron also has a spin and therefore should be considered as a tiny magnet. In presence of an external magnetic field, the spin can interact by aligning (lowering of energy) with the magnetic field if the spin is in one direction. The opposite alignment results in an increase in the energy. Thus, a fourth quantum number must be introduced to define the spin of the electron. Since there can be only two directions of spin, ‘clockwise' and ‘anti-clockwise', the spin quantum number ms can take values + ½ or -½. The electron is a quantum mechanical object and not a sphere. There is no classical analogue of a spinning electron and the words spin, clockwise and anticlockwise should not be taken literally. No one has actually "seen" a spinning electron!
is single valued, continuous and finite. The energy E of Eq 4.5 depends explicitly on n and the quantum numbers ml and l explicitly appear only in Eqs. 4.3 and 4.4. 
