Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Franz Schwabl Quantum Mechanics 4th Edit · Problem 9.3
Addition of Angular Momenta
Physics — Quantum Mechanics · spin-eigenstates-rotation
Problem Show that the states
∣ e , ± ⟩ = e − i α S y / ℏ { ∣ ↑ ⟩ ∣ ↓ ⟩ |\boldsymbol{e}, \pm\rangle = \mathrm{e}^{-\mathrm{i}\alpha S_y/\hbar}\begin{cases}|{\uparrow}\rangle \\ |{\downarrow}\rangle\end{cases} ∣ e , ± ⟩ = e − i α S y /ℏ { ∣ ↑ ⟩ ∣ ↓ ⟩ e = ( sin α , 0 , cos α ) . \boldsymbol{e} = (\sin\alpha, 0, \cos\alpha) \;. e = ( sin α , 0 , cos α ) . S ′ = e − i α S y / ℏ S e i α S y / ℏ \boldsymbol{S}' = \mathrm{e}^{-\mathrm{i}\alpha S_y/\hbar}\, \boldsymbol{S}\, \mathrm{e}^{\mathrm{i}\alpha S_y/\hbar} S ′ = e − i α S y /ℏ S e i α S y /ℏ S z ′ = S ⋅ e S'_z = \boldsymbol{S} \cdot \boldsymbol{e} S z ′ = S ⋅ e Browse the problem library