Quantum cosmology with k-Essence theory

A class of $k$-Essence cosmological models, with a power law kinetic term, is quantised in the mini-superspace. It is shown that for a specific configuration, corresponding to a pressureless fluid, a Schr\"odinger-type equation is obtained with the scalar field playing the r\^ole of time. The resulting quantum scenario reveals a bounce, the classical behaviour being recovered asymptotically.