Recursion relation for C-G coefficients

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Discussion Overview

The discussion revolves around the recursion relation for Clebsch-Gordan coefficients as presented in J.J. Sakurai's "Modern Quantum Mechanics." Participants are examining specific equations and conditions under which these coefficients vanish or do not vanish, seeking clarification on the underlying principles and examples provided in the text.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions why the terms in the recursion relation do not vanish despite the condition that Clebsch-Gordan coefficients vanish unless m = m1 + m2.
  • The same participant seeks clarification on why, in a specific example, m1 + m2 = m.
  • Another participant confirms the source of the discussion is "Modern Quantum Mechanics" by J.J. Sakurai.
  • A further participant inquires about the edition of the book being referenced.
  • It is noted that the edition in question is the revised edition printed in 2005.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing confusion and seeking clarification on specific points without reaching a consensus.

Contextual Notes

Participants have not provided detailed assumptions or definitions that may affect the interpretation of the recursion relation or the conditions for the Clebsch-Gordan coefficients.

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From J.J. Zakurai page no.222-225:

We know that Clebsch-Gordan coefficients vanish unless m=m1+m2. Then,

(1) why is that the terms in recursion relation doesn't vanish? since m1+m2=m+1 or m1+m2=m-1 in eqn.(3.7.49).

(2) why is again in the example shown in eqn.(3.7.54), m1+m2=m?

I couldn't understand the whole thing. Somebody please help.
 
Physics news on Phys.org
Excuse me, the book is- "Modern Quantum Mechanics" by J.J. Sakurai
 
what edition?
 
It is the 'revised edition' printed in 2005.
 

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