  Equivalent relations between quantum mechanical systems in the
Robertson-Walker (RW) background metric and quantum dynamics with an induced
quadratic background potential are derived in this work. Two elementary
applications, which include an algebraic derivation of the evolution operator
for a simple harmonic oscillator without using any special function or the path
integral technique, and a moving soliton solution of a free particle in an
oscillating universe, are presented to illustrate the use of these equivalent
relations.

High Energy Physics - Theory