Abstract
Because wave functions play a central role in nonrelativistic quantum mechanics, one method of combining quantum mechanics and special relativity takes the form of efforts to construct relativistic wave functions. This paper outlines how it is now possible to construct harmonic oscillator wave functions without time-like excitations which form the vector spaces for the unitary irreducible representations of the Poincaré group. Some experimental verifications for the validity of this wave function are summarized.
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