Spin Precession

Bloch sphere — spin-½ in a magnetic field, Larmor precession and Rabi oscillations

Magnetic Field

B field (Larmor ω) 1.0

Oscillating B₁ 0.0

Drive frequency 1.0

T₂ relaxation ∞

⟨Sx⟩: 0.00

⟨Sy⟩: 0.00

⟨Sz⟩: 1.00

|ψ|²: 1.00

Bloch vector traces the spin state on the unit sphere. z-axis = quantization axis (B₀). The Larmor frequency ω = γB₀.

When B₁ is resonant (ω_drive = ω_Larmor), Rabi oscillations flip the spin — the basis of NMR and MRI.