What are the equations for angular momentum?

Click For Summary
SUMMARY

The discussion centers on the equations for angular momentum as presented in Sakurai's text. Participants clarify that the transition between the equations involves basic algebraic manipulation, specifically the distributive property: A(pq + rs)B = ApqB + ArsB. Additionally, they reference the eigenvalue equations Sz|+> = |+> and Sz|-> = -|->, which are crucial for understanding angular momentum in quantum mechanics. The use of the exponential function's expansion definition is also highlighted as a key concept in this context.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly angular momentum.
  • Familiarity with algebraic manipulation and the distributive property.
  • Knowledge of eigenvalues and eigenvectors in quantum systems.
  • Basic comprehension of exponential functions and their expansions.
NEXT STEPS
  • Study the derivation of angular momentum operators in quantum mechanics.
  • Learn about the significance of eigenvalues and eigenvectors in quantum states.
  • Explore the properties of the exponential function in quantum mechanics.
  • Review Sakurai's "Modern Quantum Mechanics" for deeper insights into angular momentum.
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, as well as educators seeking to clarify concepts related to angular momentum.

AdrianMay
Messages
121
Reaction score
4
Hi folks,

The attachment is from Sakurai where he's getting started on angular momentum. I don't understand how he gets between the two equations I stuck a ? on. Any hints gratefully appreciated.

Adrian.
 

Attachments

  • sak.GIF
    sak.GIF
    12.4 KB · Views: 513
Physics news on Phys.org
Hi Adrian! :smile:

It's ordinary algebra …

A(pq + rs)B = ApqB + ArsB,

together with Sz|+> = |+>, Sz|-> = -|->, and the expansion definition of exp :wink:
 
I swear the exact same question was on this forum or the HW:Advanced Physics 2 weeks ago.
 

Similar threads

High School How to show that particle spin includes angular momentum?
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Robertson uncertainty relation for the angular momentum components
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Understanding tensor product and direct sum
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad What do you need to establish that spin is conserved?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Addition of angular momenta
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Exploring the Lamb Shift: G-Factor & Angular Momentum
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Potential between Photons via Delbruck Scattering
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Are certain combinations of quantum numbers (basis vectors) forbidden?
  • · Replies 1 ·
Replies
1
Views
1K
High School Is angular momentum of a quantum object, metaphorical?
  • · Replies 28 ·
Replies
28
Views
3K
Graduate Conservation of angular momentum in positron-electron annihilation
  • · Replies 3 ·
Replies
3
Views
3K