Abstract
Exact physical solutions to the Schrödinger stationary state equation are reported for local, relativistic, real scalar theories featuring an interaction energy density of the form g |φ|2N, where the coupling constant g is positive and the exponent N is a constant parameter (not necessarily an integer) greater than unity. No interaction or scattering between the field quanta is manifest in the multiparticle state solutions, implying that the real scalar theories are effectively linear in the absence of mass or coupling constant renormalization.
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