2状態系
E I = 1 2 ( H 11 + H 22 ) + 1 2 ( H 11 − H 22 ) 2 + 4 | H 12 | 2 {\displaystyle E_{I}={\frac {1}{2}}(H_{11}+H_{22})+{\frac {1}{2}}{\sqrt {(H_{11}-H_{22})^{2}+4|H_{12}|^{2}}}}
E I I = 1 2 ( H 11 + H 22 ) − 1 2 ( H 11 − H 22 ) 2 + 4 | H 12 | 2 {\displaystyle E_{II}={\frac {1}{2}}(H_{11}+H_{22})-{\frac {1}{2}}{\sqrt {(H_{11}-H_{22})^{2}+4|H_{12}|^{2}}}}
| I ⟩ = cos  θ 2 e − i φ / 2 | 1 ⟩ + sin  θ 2 e i φ / 2 | 2 ⟩ {\displaystyle |\mathrm {I} \rangle =\cos {\frac {\theta }{2}}e^{-i\phi /2}|1\rangle +\sin {\frac {\theta }{2}}e^{i\phi /2}|2\rangle }
| I I ⟩ = − sin  θ 2 e − i φ / 2 | 1 ⟩ + cos  θ 2 e i φ / 2 | 2 ⟩ {\displaystyle |\mathrm {II} \rangle =-\sin {\frac {\theta }{2}}e^{-i\phi /2}|1\rangle +\cos {\frac {\theta }{2}}e^{i\phi /2}|2\rangle }