Observable Effects of Noncommutative Spacetime on the Hydrogen Atom.pdfVIP

OBSERVABLE EFFECTS OF NONCOMMUTATIVE SPACETIME ON THE HYDROGEN ATOM 6 0 Benjamin Katsuo Johnson1 0 2 Department of Physics n University of Maryland a J College Park, Maryland 20742 0 3 University of Maryland Preprint: PP 06-001 ] h p Abstract - d e We present a brief historical introduction to the motivations behind quan- . s c tum mechanics and quantum field theory on noncommutative spacetime and i s provide an insightful technique, readily accessible to the undergraduate stu- y h dent, to examine the measurable effects of noncommutative spacetime on the p [ familiar hydrogen atom. Finally, we compare our results to those derived from 1 more sophisticated approaches. v 4 1 2 1 1 Introduction 0 6 0 / Noncommutativity is a fundamental concept underlying quantum physics. All con- s c jugate variables fail to commute and indeed the uncertainty principle itself, i s y h¯ h (∆x)(∆p ) ≥ (1) p 2 : v is based on the commutation relation of position and momentum, i X r a [x, p] ≡ xp − px = ih.¯ (2) Quantum field theory on noncommutative spacetime is a modification of quan- tum field theory based on the conjecture that spacetime coordinates at the Planck scale do not commute. Traditionally, it is assumed that spacetime coordinates are commutative,