  We present an alternative formulation of quantum decoherence theory using
conditional wave theory (CWT), which was originally developed in molecular
physics (also known as exact factorisation methods). We formulate a CWT of a
classic model of collisional decoherence of a free particle with environmental
particles treated in a long-wavelength limit. In general, the CWT equation of
motion for the particle is non-linear, where the non-linearity enters via the
CWT gauge fields. For Gaussian wave packets the analytic solutions of the CWT
equations are in exact agreement with those from the density matrix formalism.
We show that CWT gauge terms that determine the dynamics of the particle's
marginal wave function are related to a Taylor series expansion of the
particle's reduced density matrix. Approximate solutions to these equations
lead to a linear-time approximation that reproduces the ensemble width in the
limits of both short and long times, in addition to reproducing the long-term
behaviour of the coherence length. With this approximation, the non-linear
equation of motion for the particle's marginal wave function can be written in
the form of the logarithmic Schr\"odinger equation. The CWT formalism may lead
to computationally efficient calculations of quantum decoherence, since it
involves working with wave-function level terms instead of evolving a density
matrix via a master equation.
