  Transport, separation, and merging of trapped ion crystals are essential
operations for most large-scale quantum computing architectures. In this work,
we develop a theoretical framework that describes the dynamics of ions in
time-varying potentials with a motional squeeze operator, followed by a
motional displacement operator. Using this framework, we develop a new, general
protocol for trapped ion transport, separation, and merging. We show that
motional squeezing can prepare an ion wave packet to enable transfer from the
ground state of one trapping potential to another. The framework and protocol
are applicable if the potential is harmonic over the extent of the ion wave
packets at all times. As illustrations, we discuss two specific operations:
changing the strength of the confining potential for a single ion, and
separating same-species ions with their mutual Coulomb force. Both of these
operations are, ideally, free of residual motional excitation.
