Semiclassical predictions of cosmological wave packets from ridgelines

Abstract

We introduce a concept of ridgelines to investigate the semiclassical predictions from wave packets with arbitrary widths in conventional quantum mechanics and the Wheeler--DeWitt quantum cosmology. Two primary approaches are applied to the exact calculation of the ridgelines, namely the contour and the stream approaches. Moreover, aspects of these are discussed and compared to other scenarios and approaches, i.e., the narrow WKB wave packets and the first-derivative test. As the main result, we show that the semiclassical predictions in toy models have more abundant solutions than the ones in the classical theory, and most interestingly they may deviate from classical solutions due to the quantum corrections.