Feynman's Lectures on Physics has an interesting graphic in volume 3, page 7_3, "Fig. 7-1. Relativistic transformation of the amplitude of a particle at rest in the x-t systems.", see scan below. Say ψ is the wavefunction of a particle at rest in 3D space, ψ = exp[-iEt], hbar = 1. If I now move with some velocity v the particle at rest now has some momentum so ψ --> ψ' = exp[-i(-mv.r' - Et')]? If on the other hand, instead of going some velocity v, I instead rotate say on a merry-go-round how will ψ transform? Will I say the particle now has angular momentum? Related question? What does a large field of simultaneous clocks look like from the reference frame of someone riding a merry-go round? From the three points of view,at rest, moving, and rotating, what do the hyperplanes ψ = constant look like? Feynman's graphic gives clue for the first two? Does rotation cause the hyperplanes to curve or are they "flat"? Does this problem have anything to do with the "magic" of boosts and rotations forming a group? Boosting around some point results in some rotation? Thanks for any hints or help!