Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems A Modern Approach to Quantum Mechanics · Problem 5.3
Wave Mechanics in One Dimension — John S. Townsend
Physics — Quantum Mechanics · singlet-state-arbitrary-direction-basis
Problem Express the total-spin s = 0 s = 0 s = 0 1 2 \frac{1}{2} 2 1 ∣ + n , − n ⟩ |{+\mathbf{n}}, {-\mathbf{n}}\rangle ∣ + n , − n ⟩ ∣ − n , + n ⟩ |{-\mathbf{n}}, {+\mathbf{n}}\rangle ∣ − n , + n ⟩ 1 2 \frac{1}{2} 2 1 ∣ + n ⟩ = cos θ 2 ∣ + z ⟩ + e i ϕ sin θ 2 ∣ − z ⟩ ∣ − n ⟩ = sin θ 2 ∣ + z ⟩ − e i ϕ cos θ 2 ∣ − z ⟩ \begin{aligned}
|{+\mathbf{n}}\rangle &= \cos\frac{\theta}{2}|{+z}\rangle + e^{i\phi}\sin\frac{\theta}{2}|{-z}\rangle \\
|{-\mathbf{n}}\rangle &= \sin\frac{\theta}{2}|{+z}\rangle - e^{i\phi}\cos\frac{\theta}{2}|{-z}\rangle
\end{aligned} ∣ + n ⟩ ∣ − n ⟩ = cos 2 θ ∣ + z ⟩ + e i ϕ sin 2 θ ∣ − z ⟩ = sin 2 θ ∣ + z ⟩ − e i ϕ cos 2 θ ∣ − z ⟩ Browse the problem library