Motivated by recent parallels between classical bouncing droplet experiments and quantum bound states, we explore the lessons that droplet experiments might teach us about the dynamics of quantum solutions. Since the classical experiment is periodically driven, we examine periodic driving of the integer spin Klein-Gordon equation. We find that an exact solution can be obtained, and surprisingly this solution necessarily produces “half-integer” orbital angular momentum. We stress that these findings are strictly mathematical; nevertheless, this and other physical implications are intriguing and suggest further study.