  This paper presents a new Symmetrical Theory (ST) of nonrelativistic quantum
mechanics which postulates: quantum mechanics is a theory about complete
experiments, not particles; a complete experiment is maximally described by a
complex transition amplitude density; and this transition amplitude density
never collapses. This new ST is compared to the Conventional Theory (CT) of
nonrelativistic quantum mechanics for the analysis of a beam-splitter
experiment. The ST makes several experimentally testable predictions that
differ from the CT, which can be checked using existing technology. The ST also
solves one part of the CT measurement problem, and resolves some of the
paradoxes of the CT. This nonrelativistic ST is the low energy limit of a
relativistic ST presented in an earlier paper \cite{Heaney1}.
