Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations
By L. Chang, D. Minic, N. Okamura, T. Takeuchi. 2001
300 citations recorded by the source corpus.
We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations $[{x}_{i},{p}_{j}]=i\ensuremath{\Elzxh}[(1+\ensuremath{\beta}{p}^{2}){\ensuremath{\delta}}_{\mathrm{ij}}+{\ensuremath{\beta}}^{\ensuremath{'}}{p}_{i}{p}_{j}].$ These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relations which appear in perturbative string theory. Our solutions illustrate how certain features of string theory may manifest themselves in simple quantum mechanical systems through the modification of the canonical commutation relations. We discuss whether such effects are observable in precision measurements on electrons trapped in strong magnetic fields.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ff000588517c6e427b41b3e804d099f2e3f19210
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In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Generalized Uncertainty Principle: Approaches and Applications (2014, background): “• 1-dimensional harmonic oscillator with minimal uncertainty in position [29] and minimal uncertainty in position and momentum [76] and d-dimensional harmonic oscillator with position minimal uncertainty [77, 78],”
- Minimal Length Scale Scenarios for Quantum Gravity (2012, background): “In this fashion, in the leading-order approximation, the harmonic oscillator in one dimension has been studied in [184, 167, 8, 125], the harmonic oscillator in arbitrary dimensions in [83, 177, 85, 93], the energy levels of the hydrogen atom in [167, 69, 296, 67, 258], the particle in a box in [7],”