Spin Operator

Topics

• Spin
• Pauli Spin Matrices
• Magnetic Dipole Moment
• Lamor Precession
• Clebsch-Gordan Coefficients
• Composite States

${\hat{S}}^2|s,m_s⟩={\hslash }^{2}s(s+1)|s,m_s⟩$

• ${\hat{S}}^2=⟨S_x,S_y,S_z⟩$
• $s$ is the spin of the particle
• $m_s$ is the spin quantum number
• $|s{m}_s⟩$ represents a state with a certain $s$ and $m_s$
• $\hslash$ is the [reduced Planck constant]

${\hat{S}}_z|s,m_s⟩=\hslash m_s|s,m_s⟩$

${\hat{S}}_{\pm }|s,m_s⟩=\hslash \sqrt{s(s+1)-m_s(m_s\pm 1)}|s,(m_s\pm 1)⟩$

• ${\hat{S}}_{\pm }$ is a ladder operator

${\hat{S}}_s^2={\hslash }^{2}s(s+1)I_{2s+1}$

• The operator for a particle with spin $s$ in matrix form