Effects of Minimal Length on Quantum Mechanical Scattering
Abstract
Minimal length seems to be a nearly universal concept in quantum gravity. In order to make the uncertainty principle compatible with the notion of minimal length, one must modify the uncertainty principle. This modification is known as the Generalized Uncertainty Principle (GUP). Due to this modification of the uncertainty principle; one must therefore modify the algebra generating quantum mechanics. Thus it follows that the Schrödinger equation itself must take a new form which was first shown by Kempf, Managano and Mann. In this investigation, we solved the modified Schrödinger equation for the cases of scattering from a Coulomb potential and a ``soft sphere'' and found the modification to the scattering cross section in each case.
Funded by the Michigan Space Grant Consortium.- Publication:
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APS April Meeting Abstracts
- Pub Date:
- April 2011
- Bibcode:
- 2011APS..APRB12008B