Two electrons trapped in a quantum dot each carry spin
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin
The Structure of Quantum Mechanics, Ch Adding angular momenta, tensor operators and Wigner-Eckart
Problem
Two electrons trapped in a quantum dot each carry spin 21. Electron A is prepared with spin up along z and electron B with spin down along z, so the joint state is the uncoupled product ∣↑⟩A∣↓⟩B.
((a)) Give the dimension of the joint spin space two ways: as a product of the two single-particle dimensions, and as a sum over the coupled multiplets s=1,0.
((b)) Write ∣↑⟩A∣↓⟩B in the coupled basis ∣s,ms⟩, and give the probability that a measurement of the total spin quantum number s yields 1 and the probability it yields 0.