Scattering and Bound States of a Deformed Quantum Mechanics
High Energy Physics - Theory
2012-07-09 v1 Quantum Physics
Abstract
We construct the exact position representation of a deformed quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and scattering from a step potential, among others. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well. In the process we also highlight some limitations and pit-falls of low-momentum or perturbative treatments and thus resolve two puzzles occurring in the literature.
Keywords
Cite
@article{arxiv.1207.1519,
title = {Scattering and Bound States of a Deformed Quantum Mechanics},
author = {Chee-Leong Ching and Rajesh Parwani},
journal= {arXiv preprint arXiv:1207.1519},
year = {2012}
}