In the present lecture you have been introduced to the Schrodinger equation for a hydrogen atom. The potential energy between the nucleus and electron depends on the distance r between them. Since r = (x 2 +y 2 +z 2)1/2 can not be separated in terms of x, y, and z, the kinetic energy operator which includes
is separated in spherical polar coordianates r,
and
and in these coordinates the Schrodinger eqation is separable.The three separate eqations in the variables r ,
and (Equations 4.3 , 4.4 and 4.5 ) can be solved and the solutions
(r,
, ) = Rnl(r)
()
(
) are listed in Table 4.1.
The detailed techniques for solving the r part and part will be introduced in a later course in mathematics . For the present you may substitute the solutons into the equations and verify that you get the correct values of energy and quantum numbers .
The integer values and the relationships between n, l and m l (ie l < n, | m l |
l ) are a consequence of the boundary conditions and the uncertainity principle.
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is separated in spherical polar coordianates r,
and
and in these coordinates the Schrodinger eqation is separable.The three separate eqations in the variables r ,
(r,
(
(
) are listed in Table 4.1. 
l ) are a consequence of the boundary conditions and the uncertainity principle. 
