2000/01/17 by H. N. Núñez‐Yépez, Núñez-Yépez, H. N., E. Guillaumı́n-España +5
Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Physics (physics.gen-ph) #Physics Education (physics.ed-ph)
paper · pdf · doi:10.48550/arxiv.physics/0001030
openalex publication_date 2000/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In this work, we give an introduction to quantum mechanics in momentum space, where the Schrödinger equation becomes an integral equation. To this end we discuss standard problems, namely, the free particle, the quantum motion under a constant potential, a particle interacting with a potential step, and the motion of a particle under a harmonic potential. What is not so standard is that they are all conceived from momentum space and hence they, with the exception of the free particle, are not equivalent to the coordinate space ones with the same names. All the problems are solved within the momentum representation making no reference to the systems they correspond to in the coordinate representation.