arXiv subjects
Publications and source records attributed to Sandor Benczik.
The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i, P_j] = i\hbar\{δ_{ij}(1+βP^2) + β'P_iP_j\}$ is determined both numerically and perturbatively for arbitrary values of $β'/β$ and angular momenta $\ell$. The constraint on the minimal length scale from precision hydrogen spectroscopy data is of order of a few GeV$\null^{-1}$, weaker than previously claimed.
We study the phenomenological implications of the classical limit of the "stringy" commutation relations [x_i,p_j]=i hbar[(1+beta p^2) delta_{ij} + beta' p_i p_j]. In particular, we investigate the "deformation" of Kepler's third law and apply our result to the rotation curves of gas and stars in spiral galaxies.
We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.