Simple quantum systems in the momentum representation

The momentum representation is little used in quantum mechanics courses. So me students are hence surprised by the change in viewpoint when, in doing a dvanced work, they have to use the momentum rather than the coordinate repr esentation. In this work, we give an introduction to quantum mechanics in m omentum spate. To this end we discuss standard "elementary" problems, namel y, the free particle, the quantum motion under a constant potential functio n, a particle interacting with a potential step function, and the motion of a particle under a oscillatory potential function. What is not standard is that they are all conceived from momentum space and hence they, with the e xception of the free particle, are not equivalent to the coordinate space o nes with the same names. We solve for the bound eigenstates of the problems working within the momentum representation trying not to make explicit ref erence to the systems they correspond to in the coordinate representation.