Surprises in the suddenly-expanded infinite well

Abstract

I study the time-evolution of a particle prepared in the ground state of an infinite well after the latter is suddenly expanded. It turns out that the probability density $|\Psi (x,t){|}^2$ shows up quite a surprising behaviour: for definite times, {\it plateaux} appear for which $|\Psi (x,t){|}^2$ is constant on finite intervals for $x$. Elements of theoretical explanation are given by analyzing the singular component of the second derivative ${\partial }_{xx}\Psi (x,t)$. Analytical closed expressions are obtained for some specific times, which easily allow to show that, at these times, the density organizes itself into regular patterns provided the size of the box in large enough; more, above some critical time-dependent size, the density patterns are independent of the expansion parameter. It is seen how the density at these times simply results from a construction game with definite rules acting on the pieces of the initial density.

24 pages, 14 figures

References in corpus (6)

• Quantum wave packet revivals
• Dynamics of a Tonks-Girardeau gas released from a hard-wall trap
• Unravelling quantum carpets: a travelling wave approach
• Talbot Oscillations and Periodic Focusing in a One-Dimensional Condensate
• Unusual quantum states: nonlocality, entropy, Maxwell's daemon, and fractals
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Cited by in corpus (3)

• Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
• Joule expansion of a pure many-body state
• Quantifying the failure of Schrödinger dynamics in the free expansion of relativistic particles