The component of the total spin in the direction of H

Click For Summary
SUMMARY

The total spin component in the direction of an external magnetic field H is defined as \( M_s = \frac{1}{2}(N_{up} - N_{down}) \). In this equation, \( N_{up} \) represents the number of particles with spin up, contributing \( +1/2 \) to the total magnetization, while \( N_{down} \) represents the number of particles with spin down, contributing \( -1/2 \). This relationship is fundamental in understanding magnetic properties in quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with spin and magnetization concepts
  • Knowledge of particle statistics in physics
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Study the principles of quantum spin and its implications in magnetism
  • Explore the role of external magnetic fields in quantum systems
  • Learn about particle statistics, specifically Fermi-Dirac and Bose-Einstein statistics
  • Investigate applications of spin in quantum computing technologies
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, magnetism, and materials science.

Another
Messages
104
Reaction score
5
323.png


i don't understand,
Why The component of the total spin in the direction of H is ##M_s = \frac{1}{2}(N_{up}-N_{down})##
 

Attachments

  • 323.png
    323.png
    17.6 KB · Views: 714
Physics news on Phys.org
Another said:
Why The component of the total spin in the direction of H is ##M_s = \frac{1}{2}(N_{up}-N_{down})##
Because ##N_{\uparrow}## particles contribute ##+1/2## and ##N_{\downarrow}## particles contribute ##-1/2## to the total magnetisation.
 
  • Like
Likes   Reactions: Another

Similar threads

Undergrad Confused about a matrix element
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Symmetry and two electron wave function
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Double Check Normalization Condition
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Coleman: "Spin is a concept that applies only to particles with mass"
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Question about Stern-Gerlach experiment
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Determining the Number of Points in the n-Space
  • · Replies 16 ·
Replies
16
Views
2K
Undergrad Do spin operators 'appear' to commute for an entangled spin state?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why Does Spin Down Have Lower Energy Than Spin Up in a Magnetic Field?
  • · Replies 2 ·
Replies
2
Views
2K
Spatial Perturbative Hamiltonians In Systems of Identical Particles
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Number of particles in canonical ensemble
  • · Replies 9 ·
Replies
9
Views
2K