Sakurai 3.5.37: Formula for Matrix Element <j m | S^2_+ |j m >

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Discussion Overview

The discussion centers around the formula for the matrix element , with references to specific equations in Sakurai's text. Participants are seeking clarification on the relationship and derivation of this formula, particularly in relation to equation 3.5.37 and the delta function.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the formula for and references equation 3.5.37, questioning the role of the delta_j j' term.
  • Another participant cites equation 3.5.35 a, which involves the matrix element and includes delta functions for j and m.
  • A third participant suggests that the formulas discussed relate to finding the spin or angular momentum of a wave-function but seeks clarification on the original question.
  • A later reply indicates a withdrawal from the discussion without further elaboration.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express different levels of understanding and focus on various aspects of the equations without resolving the initial inquiry.

Contextual Notes

Participants do not clarify the assumptions behind the delta functions or the specific context of the matrix element in question, leaving some aspects of the discussion unresolved.

Nusc
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Does anyone know what the formula is for the following:

<j m | S^2_{+} |j m > = ?

Reference to equations in Sakurai would be helpful in deriving the relation. I would suspect 3.5.37 but what about the delta_j j' ?

Does anyone know what I'm talking about?
 
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3.5.35 a

<j',m|J^2 |j,m> = j(j+1)hbar^2 delta_j j' delta m m'

3.5.37 is

J_+ |j,m> = c_jm^+ |j,m+1>
 
These appear to be formulas for finding the spin, and or angular momentum, of a wave-function. What is your question exactly?
 
nevermind.
 

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