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Nuclear Magnetic Resonance

The phenomenon where nuclei absorb energy at specific frequencies when subjected to a magnetic field, leading to the generation of NMR spectra.
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The statement of the theorem

Consider a nucleus with spin angular momentum I\mathbf{I} placed in a static external magnetic field B0=B0z^\mathbf{B}_0 = B_0 \hat{\mathbf{z}}. The system Hamiltonian H\mathcal{H} is given by: H=H0−γI⋅B(t)\mathcal{H} = \mathcal{H}_0 - \gamma \mathbf{I} \cdot \mathbf{B}(t) where γ\gamma is the gyromagnetic ratio and B(t)\mathbf{B}(t) is the time-dependent magnetic field. The resonance condition occurs when the applied oscillating field B1(t)=B1cos⁡(ωt)x^\mathbf{B}_1(t) = B_1 \cos(\omega t) \hat{\mathbf{x}} matches the Larmor frequency ω0\omega_0: ω0=γB0\omega_0 = \gamma B_0 The energy absorbed by the nucleus is quantized at this frequency, leading to transitions between spin energy levels.
Source: Wikipedia