- The Resonance Condition

The Resonance Condition

Consider an isolated nucleus in a steady magnetic field $H_{_{0}}$. The magnetic field breaks the symmetry of free space and defines a particular spatial direction. Suppose that the nucleus possesses an intrinsic "spin" with spin number Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I>0} so that it has a magnetic moment. We know from quantum mechanics that (on small enough scales) energy appears in discrete bits ( Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hbar} shows its face ). It is then reasonable to suppose that "spin" energies are also discrete (or quantized). Physical experiments bear out this supposition.

The nucleus will have different energy states depending on the magnitude and direction of the nucleon's magnetic moment (see figure below).

We can define Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu} as the maximum measurable (observable) component of the magnetic moment.