Matrix elements of Hamiltonian include Dirac delta term

  • #1
MaestroBach
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TL;DR Summary
Currently reading a textbook on non-equilibrium green's functions and I'm stuck in chapter 1 where it recaps just general quantum mechanics because of dirac deltas included in the matrix elements of a generalized hamiltonian.
Currently reading a textbook on non-equilibrium green's functions and I'm stuck in chapter 1 where it recaps just general quantum mechanics because of dirac deltas included in the matrix elements of a generalized hamiltonian.

The textbook gives this:
Screenshot 2024-07-01 145152.png

I just don't understand how to think about the dirac deltas in this case, given that as far as I understand, it'll be a function that's 0 everywhere except where r = r' at which point it's equal to infinity.

For whatever reason, I can't get latex to work right now, but x = r * sigma, where sigma is the spin quantum number.
 

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