Is the Formula for Spin Also True for Angular Momentum?

Click For Summary
SUMMARY

The formula for spin, represented as S=0.5*h*σ, does not apply to orbital angular momentum (L) or total angular momentum (J). Orbital angular momentum is defined by the equation L = Q × P, where Q and P adhere to the Heisenberg commutation relations. This distinction leads to the restriction that only integer eigenvalues are permissible for orbital angular momentum. For further details, refer to Ballentine, pages 169-170.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with angular momentum operators
  • Knowledge of Lie algebra and Lie groups
  • Proficiency in Heisenberg commutation relations
NEXT STEPS
  • Study the properties of angular momentum in quantum mechanics
  • Explore Lie algebra applications in physics
  • Review the Heisenberg uncertainty principle in detail
  • Read Ballentine's "Quantum Mechanics" for in-depth analysis
USEFUL FOR

Physicists, quantum mechanics students, and researchers focusing on angular momentum and its mathematical foundations will benefit from this discussion.

Cosmossos
Messages
100
Reaction score
0
Hello
Here is the known formula for the spin: S=0.5*[STRIKE]h[/STRIKE]*\sigma
is this formula correct also to the orbital Angular momentum (L) and to the total Angular momentum?
I think it is correct because S,L,J operators that belong to Lie algebra/group.
Is it true?
 
Physics news on Phys.org
Cosmossos said:
Here is the known formula for the spin: S=0.5*[STRIKE]h[/STRIKE]*\sigma
is this formula correct also to the orbital Angular momentum (L) and to the total Angular momentum?
I think it is correct because S,L,J operators that belong to Lie algebra/group.
Is it true?

No. The orbital angular momentum has a special form:

<br /> {\bm L} ~=~ {\bm Q} ~\times~ {\bm P}<br />

where Q and P satisfy the usual Heisenberg commutation relations.
This extra restriction causes a corresponding restriction in the
possible eigenvalues of orbital angular momentum, namely that
only integer values are allowed.

Details can be found in Ballentine, pp169-170.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
View full post »

Similar threads

Graduate Coleman: "Spin is a concept that applies only to particles with mass"
  • · Replies 11 ·
Replies
11
Views
1K
Undergrad Exchange symmetry of two particles on a sphere
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How Does Position Interact with Spin Angular Momentum in Quantum Mechanics?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Addition of angular momenta
  • · Replies 1 ·
Replies
1
Views
947
Undergrad Robertson uncertainty relation for the angular momentum components
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Are certain combinations of quantum numbers (basis vectors) forbidden?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Exploring the Lamb Shift: G-Factor & Angular Momentum
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Does a free electron have an orbital magnetic moment?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Dirac equation in the hydrogen atom
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why is m_j not a good quantum number in strong-field Zeeman effect?
  • · Replies 2 ·
Replies
2
Views
2K