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I am trying to study green's function by using a lecture by NPTEL its link is https://www.youtube.com/watch?v=ZJ7v6VZQ32k&t=439s I don't get this step by him at the minute of ten.

$$D_x G(x,x^{'}) =\langle x|x'\rangle =\delta (x-x').$$

Please give your precious little time to help me

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  • $\begingroup$ Are you asking about the first or second equality? $\endgroup$ – Qmechanic Jun 5 at 8:46
  • $\begingroup$ first equality, $\endgroup$ – Robin Raj Jun 5 at 9:01
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    $\begingroup$ What do you think is missing in Prof. Balakrishnan's argument? $\endgroup$ – Qmechanic Jun 5 at 10:35
  • $\begingroup$ I don't get how position representation of some operator operates on position representation of inverse of that operator gives inner product of x with x' $\endgroup$ – Robin Raj Jun 5 at 17:39
  • $\begingroup$ An operator times its inverse yields the identity, which, in the position representation, is visibly the position delta function, no? $\endgroup$ – Cosmas Zachos Jun 6 at 0:31

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