Quantum Mechanics - Leonard Susskind on Integration by Parts

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Discussion Overview

The discussion revolves around the application of integration by parts as presented in Leonard Susskind's Quantum Mechanics lecture series. Participants are examining the specific formulation used in the context of wavefunctions and the implications of boundary conditions on the integration process.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes a discrepancy in the integration by parts formula presented by Susskind, suggesting that a term is missing from the right-hand side of the equation.
  • Another participant explains that the "FG" term is evaluated at the boundary and assumes that boundary conditions could cause this term to vanish.
  • A subsequent participant seeks clarification on what boundary conditions might lead to the vanishing of the term.
  • Another participant responds by indicating that if F or G is a wavefunction, the boundary condition could be that the wavefunction approaches zero at infinity.
  • A final participant expresses relief after receiving clarification on the matter.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the integration by parts formulation, with some expressing confusion and others providing explanations regarding boundary conditions. The discussion remains unresolved regarding the initial claim about the missing term.

Contextual Notes

There are assumptions regarding the boundary conditions that are not fully articulated, and the specific context of the wavefunction's behavior at infinity is not detailed.

Jonnyb42
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I'm watching the video series on Quantum Mechanics taught by Leonard Susskind, (from Stanford).

On Lecture #3, Dr. Susskind says that integration by parts is:

∫FG' = -∫GF'

However from what I know integral by parts to be, there i missing a +FG on the righthand side, or something... since I don't recognize that as the same as
∫FdG = FG - ∫GdF

The specific function that was being dealt with was the wavefunction ψ, (where F = G = ψ) so maybe that could have to do with it... I don't think ψ^2 = 0 though.

Thanks
 
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The "FG" part is evaluated at the boundary. I assume there are boundary conditions that make that term vanish.
 
He mentioned something about boundary conditions, could you explain to me what you mean? What boundary conditions could make the term vanish?
 
If F or G is some wavefunction ψ then the boundary condition says that ψ goes to 0 at x = + or - infinity.
 
Right ok thanks, I lost my mind there a little bit!
 

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