Quantum dynamics in a time-dependent cylindrical trap

• Motion of a quantum particle is considered in a time-dependent cylindrical trap.
• Transients corresponding to the expansion or contraction of the trap are studied.
• The density profile in the time resembles the diffraction-in-time pattern, with an enhanced fringe visibility.
• Explicit expressions for the excitations are given.

Solutions to the Schrödinger equation are examined for a particle inside a cylindrical trap of a circular time-dependent cross-section. Analytical expressions for energy and momentum expectation values are derived with respect to the exact solutions; and the adiabatic and sudden change of the boundary are discussed. The density profile as a function of time in a given observation point, resembles the diffraction-in-time pattern observed in a suddenly released particle but with an enhanced fringe visibility. Numerical computations are presented for both contracting and expanding boxes.