Angular momentum - integer or half-integer

Click For Summary
SUMMARY

The discussion clarifies the nature of angular momentum in quantum mechanics, specifically addressing total angular momentum (J), orbital angular momentum (L), and intrinsic momentum (spin, S). It establishes that orbital momentum (L) must be an integer due to the one-valuedness of wave functions, while total momentum (J) can be either integer or half-integer. Both J and S can take half-integer values, with specific constraints on S based on the value of J. For example, when J=1, S can be -1, 0, or 1, and when J=1/2, S can be -1/2 or 1/2.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with angular momentum operators
  • Knowledge of wave function properties
  • Basic grasp of particle physics and spin
NEXT STEPS
  • Study the mathematical formulation of angular momentum in quantum mechanics
  • Explore the implications of wave function one-valuedness in quantum systems
  • Investigate the role of spin in particle classification
  • Learn about the significance of half-integer and integer values in quantum states
USEFUL FOR

Students and professionals in physics, particularly those focused on quantum mechanics, particle physics, and angular momentum theory.

paweld
Messages
253
Reaction score
0
Let J be total angular momentum, L - orbital angular momentum and S - intristic momentum (spin). Squares of these operators have appropriate eigenvalues j(j+1), l(l+1), s(s+1). Which of these numbers j,l,s should be integer. I know that spin can have half-integer values. But probably orbital or total momentum values should be integer. Thanks for answer.
 
Physics news on Phys.org
The orbital momentum value must be integer. It results from the wave function one-valuedness.
The total momentum value can be half-integer.
 
j and s can both be half integer. j is one of the numbers that labels a particle species. The s of a specific particle can only change by integer amounts, and since the lowest possible value of s is always -j and the highest always +j, this means that j must be integer or half integer.

Examples: When j=1, s can take the values -1,0,1. When j=1/2, s can take the values -1/2,1/2.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K