2状態系
量子状態
| ψ ( t ) ⟩ = c 1 ( t ) | 1 ⟩ + c 2 ( t ) | 2 ⟩ ( | c 1 ( t ) | 2 + | c 2 ( t ) | 2 = 1 ) {\displaystyle |\psi (t)\rangle =c_{1}(t)|1\rangle +c_{2}(t)|2\rangle \quad (|c_{1}(t)|^{2}+|c_{2}(t)|^{2}=1)}
の時間発展はシュレディンガー方程式
i ħ ∂ ∂ t | ψ ( t ) ⟩ = H ^ | ψ ( t ) ⟩ {\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }
に従うことから、時間発展は複素係数 c1, c2 の微分方程式
i ħ d d t c 1 ( t ) = H 11 c 1 ( t ) + H 12 c 2 ( t ) {\displaystyle i\hbar {\frac {\mathrm {d} }{\mathrm {d} t}}c_{1}(t)=H_{11}c_{1}(t)+H_{12}c_{2}(t)}
i ħ d d t c 2 ( t ) = H 21 c 1 ( t ) + H 22 c 2 ( t ) {\displaystyle i\hbar {\frac {\mathrm {d} }{\mathrm {d} t}}c_{2}(t)=H_{21}c_{1}(t)+H_{22}c_{2}(t)}
で与えられる。