Two-Level Systems by Hand
Exercises
Introductory Quantum Mechanics › Unit 3 · Two-level systems & spin-1/2
Two-Level Systems by Hand
Reduce any near-degenerate pair to a 2×2 Hamiltonian, then read the physics out of E± = Ē ± √(Δ²+V²) and the mixing angle. 9 problems, one per page — start with the worked example, then work down.
- 1 worked The ammonia doublet in an electric field →
- 2 practice Every MRI magnet has a frequency printed on it →
- 3 practice A neutrino changes flavor over 500 km →
- 4 practice Bonding and antibonding are not symmetric partners →
- 5 practice Magnetic quenching of positronium →
- 6 practice Why qubits are operated at the sweet spot →
- 7 practice Timing a π-pulse →
- 8 check Two pendulums on a spring →
- 9 check Why levels refuse to cross →