Module 1 : Atomic Structure
Lecture 3 : Angular Momentum
 
   ( 2 / x 2 + 2 / y 2 ) = 1/ r 2 2 / 2 (3.3)
    The relations used are
  
x = r cos y = r sin / x = ( r / x ) /r + ( / x ) / (3.4)
 

A similar relation can be written for / y. The Schrodinger equation for K.E. becomes

 
( - 2 /2mr 2) 2 / 2 = E (3.5)
The operator for z component of angular momentum is
 
l z = y p z – z p y ( y / i ) / z - ( z / i ) /y (3.6)

and in polar coordinates , this becomes

 
l z = ( / i ) / (3.7)
This is one of the simplest forms for an operator.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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