Whether quantum state transitions occur by instantaneous
jumps
(a la Bohr) or deterministic dynamics (Schrödinger’s
preference) has been intensely debated. Recent experimental measurements
of shelved electrons have reignited the debate. We examine aspects
of the time-dependent numerical solutions of the Schrödinger
equation in quantum systems with two and three levels perturbed by
a sinusoidal field. A geometrical construction involving quantum state
phase differences illuminates the role of interstate phase differences
in a deterministic, rather than random, process of multiphoton absorption.
Alternate halves of the Rabi cycle exhibit phase reversals much like
the classical beats of coupled oscillators. For non-zero detuning,
population inversion does not occur because the exciting field drifts
out of the proper phase before inversion is complete. A close correspondence
with classical, coupled oscillator beats offers insights for interpretation
of deterministic quantum dynamics and suggests an experimental test
for the correctness of this picture depending on the long-time phase
stability of exciting fields.