  The free expansion of a Gaussian wavepacket is a problem commonly discussed
in undergraduate quantum classes by directly solving the time-dependent
Schrodinger equation as a differential equation. In this work, we provide an
alternative way to calculate the free expansion by recognizing that the
Gaussian wavepacket can be thought of as the ground state of a harmonic
oscillator with its frequency adjusted to give the initial width of the
Gaussian, and the time evolution, given by the free-particle Hamiltonian, being
the same as the application of a time-dependent squeezing operator to the
harmonic oscillator ground state. Operator manipulations alone (including the
Hadamard lemma and the exponential disentangling identity) then allow us to
directly solve the problem. As quantum instruction evolves to include more
quantum information science applications, reworking this well known problem
using a squeezing formalism will help students develop intuition for how
squeezed states are used in quantum sensing.

Quantum Physics