Page 304 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics
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Dirac delta function                      295
                                                …
                                                  f (r)ä(r ÿ r 0 )dr ˆ f (r 0 )
                        or, equivalently
                                …… …
                                    f (x, y, z)ä(x ÿ x 0 )ä(y ÿ y 0 )ä(z ÿ z 0 )dx dy dz ˆ f (x 0 , y 0 , z 0 )
                        where the range of integration includes the points x 0 , y 0 , and z 0 . The integral
                        representation is
                                                          1  … 1
                                              ä(r ÿ r 0 ) ˆ     e ik(rÿr 0 )  dk           (C:7)
                                                        (2ð) 3
                                                              ÿ1
                        where k is a vector with components k x , k y , and k z and where
                                                    dk ˆ dk x dk y dk z
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