Quantum Dynamics and Non-Inertial Frames of Reference. I: Generality

The general framework of a time-dependent scale transformation as applied to non-relativistic time-dependent Schrödinger equations is described. The nature of the transformation is clarified by comparing it with a time-dependent translation and rotation. Particular attention is paid to the associated gauge transformation and the resulting harmonic inertial force. Corresponding classical results are also displayed. This work intends to pave the way for various applications to be presented in the subsequent papers of this series.