The structural, mechanical, electronic and optical properties of SrTMO3 (TM = Rh, Zr) compounds are investigated by using first principle calculations based on density functional theory (DFT). The exchange-correlation potential was treated with the generalized gradient approximation (GGA) for the structural properties. Moreover, the modified Becke-Johnson (mBJ) approximation was also employed for the electronic properties. The calculated lattice constants are in good agreement with the available experimental and theoretical results. The elastic constants and their derived moduli reveal that SrRhO3 is ductile and SrZrO3 is brittle in nature. The band structure and the density of states calculations with mBJ-GGA predict a metallic nature for SrRhO3 and an insulating behavior for SrZrO3. The optical properties reveal that both SrRhO3 and SrZrO3 are suitable as wave reflectance compounds in the whole spectrum for SrRhO3 and in the far ultraviolet region (FUV) for SrZrO3.

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 [x,p] = ih 1 + ηp 2 . 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) ∼ so(2, 1) algebra is satisfied by the operatorsL ± andL z .

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