(a) A particle sits in the ground state of an infinite square well of width . The…
PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Quantum dynamics and its formulations · Quantum dynamics and its formulations
The Structure of Quantum Mechanics, Ch Slow change, sudden change and the Berry phase
Problem
(a) A particle sits in the ground state of an infinite square well of width L. The right-hand wall is suddenly moved outward so the well width doubles to 2L ("suddenly" meaning the wall motion is much faster than any timescale ℏ/ΔE of the particle). The wave function has no time to change during the jump. Using the sudden approximation, compute the probability that the particle is found in the new ground state immediately afterwards. (b) A spin-one-half magnetic moment is carried once around a circular path that is a cone of half-angle β=150∘ in the direction of the applied field, traversed slowly enough that the adiabatic theorem applies. Compute the geometric (Berry) phase γ+ acquired by the state with spin along the field, reduced to the range (−π,π], and compare it with the result for a cone of half-angle 30∘.