  We prove sharp lower bounds on the spectral gap of 1-dimensional
Schr\"odinger operators with Robin boundary conditions for each value of the
Robin parameter. In particular, our lower bounds apply to single-well
potentials with a centered transition point. This result extends work of Cheng
et al. and Horv\'ath in the Neumann and Dirichlet endpoint cases to the
interpolating regime. We also build on recent work by Andrews, Clutterbuck, and
Hauer in the case of convex and symmetric single-well potentials. In
particular, we show the spectral gap is an increasing function of the Robin
parameter for symmetric potentials.
