Help with the derivative of the Dirac delta

[Delerion24]

Homework Statement

Try developed this expression

Relevant Equations

The equations are in the images

My goal is to develop the equation 21. You should asume that \delta(r_2-r_1)^2 =0. These is named renormalization. Then my question is , do my computes are correct with previous condition ?

 

[berkeman]

@Delerion24 -- Please make it a habit to post your work at PF using LaTeX, not via images. You can click on the "LaTeX Guide" link below the Edit window for our LaTeX tutorial. What software did you use to write the equations in your image? Perhaps it is easy to port your work to LaTeX and add that as a reply? Thanks.

 

[WWGD]

I guess this is a Distributional derivative, or there's something else I'm not aware of here? I mean, are we referring to the Dirac delta Distribution. i.e., Generalized function?

 

[strangerep]

Homework Statement: Try developed this expression
Relevant Equations: The equations are in the images

View attachment 314422View attachment 314423

My goal is to develop the equation 21. You should asume that \delta(r_2-r_1)^2 =0. These is named renormalization.

No, the square of a delta distribution is undefined.
Where did your eq(21) come from? You say that it "is" (8b). But then later you say that eq(26) is 8b. Then you say "9 isn't 2", which I guess refers to other equations you haven't shown.

It's very hard to help when you all you show us is a mis-sequenced, incomplete, mess.

 

[sharmast]

I just started reading about holomorphic functions, maybe switch to complex coordinates and integrate around a contour. If you expand your Schrödinger equation correctly, then you should just see the wave function with a time evolution operator, like a decaying exponential tacked on the side. Let me think about this one.