Geometric Quantum Mechanics
Two state vectors differing only by a nonzero complex factor represent the same pure quantum state. Explore each principle from mathematical definition to physical evidence and limitations.
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Concept 09Projective Hilbert spaceTwo state vectors differing only by a nonzero complex factor represent the same pure quantum state.Concept 10Berry phase and adiabatic evolutionA slowly transported eigenstate acquires a geometric phase in addition to its dynamical phase.Concept 11Berry curvature as effective magnetic fieldBerry curvature plays the role of a magnetic field in parameter or momentum space.Concept 12Holonomy and Wilson loopsParallel transport around a closed path can rotate a quantum state or a degenerate subspace.Concept 13Aharonov–Bohm phaseA charged quantum wavefunction responds to enclosed magnetic flux even along paths with zero local magnetic field.Concept 14Fubini–Study quantum metricQuantum states have a natural notion of distance that measures how quickly distinguishable states change.