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arXiv · 1207.1519

Scattering and Bound States of a Deformed Quantum Mechanics

Chee-Leong Ching·Rajesh Parwani
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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.

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Chee-Leong Ching, Rajesh Parwani. 2012-07-06. Scattering and Bound States of a Deformed Quantum Mechanics. https://arxiv.org/abs/1207.1519

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