Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation
- Publication Type
- Original research
- Authors
We derive the relativistic energy spectrum for the modified Dirac equation by
adding a harmonic oscillator potential where the coordinates and momenta are
assumed to obey the commutation relation
$\left[\hat{x},\hat{p}\right]=i\hbar\left(1+\eta p^2\right)$. In the
nonrelativistic limit, our results are in agreement with the ones obtained
{previously}. Furthermore, the extension to the construction of creation and
annihilation operators for the harmonic oscillators with minimal length
uncertainty relation is presented. Finally, we show that the commutation
relation of the $su(1, 1)\sim so(2,1)$ algebra is satisfied by the {operators
$\hat{\mathcal{L}_{\pm}}$ and $\hat{\mathcal{L}_{z}}$}.
Journal
- Title
- International Journal of Modern Physics E
- Publisher
- World Scientific (Singapore)
- Publisher Country
- Singapore
- Publication Type
- Prtinted only
- Volume
- 24
- Year
- 2015
- Pages
- --